J. B. Taylor – Session II

Taylor:

Before we resume, I’d just like to make one or two comments about what I said yesterday, just for clarification. I remarked that I thought that the classified nature of the weapons program at Aldermaston, contrary to popular opinion, had helped the program, because people’s minds were concentrated on the matters in hand. I should have gone on to say that whilst I believe that to be the case for a short-term program like the hydrogen bomb project, I was not suggesting that classification and secrecy was a good thing in the long run. If I could also summarize what I think, or hope, I said yesterday concerning my contributions at AWRE, the Aldermaston weapons establishment: the important ones were the Theory of Initiation, or Predetonation, where I believe I provided a correct and convincing solution to what had been a very difficult problem; this was very satisfying because it was a problem that had first been considered by Feynman during the Manhattan Project. The second work I think was important is the Theory of the Electromagnetic Pulse, or what we called “radio flash,” and I made the point that both those contributions were amongst the first ten or so reports handed to the Americans when collaboration was resumed. And finally, I made some contributions to the design of the H-bomb, which are in Lorna Arnold’s book. I then moved into fusion. The important steps were, first the ZETA episode, which actually was responsible for my getting an opportunity to go into controlled fusion. Next there was the major conference at Harwell, following the ZETA episode, when pretty well all the various U.S. programs were presented by such luminaries as James Tuck, Edward Teller, and Lyman Spitzer, and so on. The third major step was the period between 1959 and 1960 when I made a number of visits to the U.S., followed by a Commonwealth Fellowship at Berkeley, during which I visited all the major U.S. labs, met most of the theorists, and indeed the experimenters, in the U.S. program. That established my understanding of the field. During that same 1959-1960 period I attended two seminal meetings. One was the first unclassified Sherwood meeting at Gatlinburg; the other was the first APS Plasma Physics Division meeting at Monterey. In addition this was when I met Dr. John Adams, Sir John Adams as he later became, who was director designate of a major new fusion laboratory at Culham. And so, on my return to England I was all set to make the move into controlled fusion at Culham. Now you would like me to carry on from there, would you?

Barth:

Yes. We look into your fusion work in the 1960s, 1970s, and 1980s. We could start out with your collaboration with Dr. Roberts on the finite larmor radius effects in plasmas?

Taylor:

That was the first fusion work we did together but I’d like to concentrate more on some more major points, if I may. Shortly after my arrival at Culham I was appointed head of the Theory Division, in succession to Bill Thompson, who had, in fact, never been an active leader and spent a lot of time away. Initially, Keith Roberts was acting division head, but possibly to some people’s surprise, he was not made division head. I would like to make clear that this was an amicable arrangement between Keith, who was my lifelong friend, and myself. It was partly to facilitate his move into computing. As I already mentioned, my instructions were, “to make Culham a center of excellence in plasma physics.” The first thing that helped to do that (though it has very little to do with fusion) is that I wrote what turned out to be an important paper on the Earth’s dynamo, which was published by the Royal Society (sponsored by Sir Edward Bullard). I showed that if the Earth’s dynamo is indeed driven by convective currents in the Earth’s interior, as everyone believes, then because of its rapid rotation there are strict constraints on the dynamo configuration. This created a puzzle because when it became possible to do numerical simulations of the dynamo they didn’t seem to fit this, although no one has been able to find any mistake in the paper. Although this was not directly connected with fusion it was important because it attracted a lot of interest, and indeed has attracted interest ever since. Only very recently a Japanese group claimed that for the first time they had done a simulation that seemed to show a configuration similar to the one I calculated in 1963. So, that’s something that has taken [Laugh] about forty years to come to fruition.

Barth:

How did you get into this question?

Taylor:

It came about indirectly because of one of the unusual features of Culham when it was set up as a new government laboratory. John Adams was a very influential and important person, having been Acting Director of CERN from 1960-1961: the Atomic Energy Authority was very pleased and keen to get him back. He was a catch, like getting the best quarter back at football. Therefore I assume he was able to lay down conditions that he wanted to have. He was very keen, after his experience at CERN, to make Culham different from other government labs. First of all, he insisted that it was totally unclassified. It was the height of the Cold War when at other government establishments security was a big issue. But at Culham there were few restrictions. It was possible for the first time for Russians, or Chinese, to come and work at a government laboratory, I don’t know exactly under what circumstances but my recollection is that the only restriction was that there weren’t to be too many of them at any one time. The second point was that the lab was completely open. People hardly believe this now when I tell them there was no guardhouse at the gate. Anyone could wander in at any time. And indeed, in the early to mid 1960s, the public bus service from Dorchester to Abingdon went through the lab and had two stops within the laboratory perimeter. This openness was an attractive feature of the lab for many years until, unfortunately, there was a major theft at the laboratory. The local chief constable was critical of the management of Culham over what he saw as lax security. Initially, the restrictions introduced were very limited, but they have been ramped up ever since and I’m afraid now it’s just like every other place. I occasionally say that security measures at Culham are now more onerous than they were when I was making hydrogen bombs at Aldermaston. [Laugh] That’s very nearly true, actually. It’s a change in the whole culture since my day. The final feature Adams introduced countered a problem of a laboratory created with people all of similar age. They just grow old there, and there’s no influx of new staff. Therefore Adams introduced the Culham Research Associate scheme, which was the nearest thing in a government lab to a Postdoc position in America. These positions were supposed to be limited to three years and the intention was there would be a continuous throughput of Culham research associates, some of whom would be the foreigners that we’ve mentioned, but many of whom would be British. He introduced this scheme in the face of opposition from the trade unions, who in Britain at that time were extremely powerful.

Barth:

What was the unions’ argument?

Taylor:

The unions argued that this was exploiting people, that we were taking their best years and not giving them a proper secure career. Anyway, John introduced this CRA scheme, and initially the idea was that twenty-five percent of the staff should be on this basis. But many of the British Culham research associates, who should have left and been replaced, just joined the permanent staff. This gave the unions another argument: they claimed that this was using the CRA scheme as an improper probation system. Whatever the true facts, the CRA scheme diminished. I don’t think it formally exists anymore, although there are similar appointments made on an ad hoc basis. The relevance of this to my dynamo work is that it came about through my contact with one of the first Culham Research Associates, Nigel Weiss. He had been a student of Bullard’s at Cambridge, working on the dynamo problem. The intention was that he should continue this work, which Keith Roberts thought would be a good vehicle to publicize and develop Culham’s computing facilities. There was one further aspect of John Adams’ vision for Culham. He insisted that every building on the site be linked to every other building by enclosed corridors so that a free exchange of views wouldn’t be inhibited because people did not want to go outside in the rain. [Laugh] So I’ve arrived at Culham and been made division head and I’ve written my first important paper — on the Earth’s dynamo. But now I have to get back to the subject of fusion. As I explained, Culham was originally planned as the home of a very large experiment called ICSE. This was based on the toroidal reverse field pinch concept that ZETA had introduced. However, this was canceled and the initial program at Culham became something quite different. It was based not on a single large pinch-type toroidal experiment, but on a number of sizeable but smaller experiments on magnetic mirrors or adiabatic confinement. The program turned decisively to these machines. I supported this change of direction as it was in accord with my belief that one should start from a vacuum magnetic field, which everybody agrees is absolutely stable, and then add the plasma gradually to see how far one can build it up before something deleterious happens. I thought this much more sensible than starting off with a great big bang, producing plasma in an uncontrolled fashion. In the 1960s the programs in many places moved in this direction, and mirror machines were quite the flavor of the year, or the month as it might be.

Barth:

Do you remember any interaction with Richard Post? Would he come to Culham to look at the machine designs?

Taylor:

I certainly had quite close contacts with Dick Post at the time and with the theorists at Livermore. There was also close contact with the Russians. The adiabatic mirror principle, which is a pretty obvious scheme, was one of the methods that had been invented almost everywhere independently, and is related to particles trapped in the ionosphere. There was a well established understanding of how mirror machines ought to operate, but actually they didn’t quite behave as they should. The problem is that in a simple axisymmetric machine there is an instability, which everyone realized was related to the fact that the magnetic field falls off with distance from the axis of the machine. (The first convincing proof of this was actually written by Rosenbluth and Longmire.) So anyway, everyone realized that this was the problem without knowing what to do about it. But then the Russians, principally Ioffe, argued that, “If the problem is related to the fact that the magnetic field falls off with radius, let’s put on a second, orthogonal, magnetic field which increases with radius.” Although it seemed an obvious idea people didn’t really like this because it made the magnetic field very complicated. However, Ioffe tried it out and had some success. Although the preliminary experiments were encouraging, the complexity of the magnetic field still put most people off. Because there was no symmetry it was very difficult to treat theoretically. I well remember sitting in on a meeting where they were arguing about how particle orbits could possibly be closed in a magnetic field of such complexity. So, although there was sympathy for the idea that if you added these two orthogonal fields it ought to help the stability problem, it made the orbits so complicated you would never be able to analyze them. The situation was confused but hopeful, because of Ioffe’s success.

Barth:

He simply got longer confinement times?

Taylor:

Yes, the confinement time improved in the Ioffe experiment, but it was complicated to analyze. It was a great surprise, therefore, when I was able to show that you could sweep all this complexity aside if you concentrated your attention on the magnetic isobars, which are the surfaces on which the field strength is constant. They are simple shapes; not like the complicated shapes that the field itself has. I was able to show mathematically that you could describe all the complex particle orbits in terms of these magnetic isobars: then you could show when there was confinement, and more importantly, when there was stable confinement. Later, with Jim Hastie, I was able to calculate how much plasma pressure you could have before the stability was lost. It was a massive simplification of the whole problem and I think it was partly responsible for the fact that a number of these combined magnetic field systems were built at Culham and elsewhere. (I rather foolishly called these systems “combined mirror cusp fields,” which is hardly a very sexy title. Harold Furth came up with a much better idea of “minimum-B,” and someone else thought of “magnetic wells.”) Two machines based on minimum-B built at Culham were MTSE II (Magnetic Trap Stability Experiment, II); and Phoenix II. A number of similar machines were built at Livermore, culminating in some very large ones, larger than any built at Culham.

Barth:

Is it then fair to regard you as the inventor of magnetic wells, or is it just a particular theoretical approach to minimum-B?

Taylor:

Credit for the invention of minimum-B must go to Ioffe, because he proposed it and did the first experiment. I think I could claim credit for having provided the theoretical backing. What I like about it is that it was very clear-cut, complete, and it has never been changed in fifty years.

Barth:

Where did the insight come from to focus on the magnetic isobars?

Taylor:

By approaching the problem with the view that we should look first at the magnetic field alone and see what properties it has, and then think about putting the plasma in. A second step was to describe the orbits in a Hamiltonian manner. Then one can show that the orbits have certain general properties without needing to examine them in detail. Without going into mathematics it’s a bit difficult to explain this. It’s really a mathematical simplification that removes all the complications that appear at first sight when you look at the problem. This was a period when things were very intensely theory driven. I believe it was very influential that I had come along with a comprehensive, convincing theory, which the experimenters could follow.

Barth:

How did the experimentalists respond? Did they say, “Yes, now we have an approach in our hands that allows us to design machines better?”

Taylor:

Some of them did, yes. [Laugh] Some of them said, “Oh, these damn theorists, I wish they’d let us just do our experiments.” [Laugh] It sounds terribly conceited but as it was fifty years ago I’m allowed to say that a couple of my experimental colleagues did say, “Thank god, Bryan, you’ve sorted all this. Now we can go ahead.” So, yes, it was well received, and it was the first step in the job that John had told me to do, namely to put Culham on the fusion map.

Barth:

Was this a widely read paper?^[1]

Taylor:

I believe it was, yes. We didn’t have things like Citation Index [Laugh] in those days, so you can’t look it up. But I think it was a big step in establishing Culham in the field.

Barth:

By this time, were you convinced of the mirror concept as the best approach?

Taylor:

At the time, probably, yes. Mainly because we felt we understood it, whereas we knew we didn’t understand the Reversed-Field Pinch (RFP). This may seem surprising because when you first look at the two configurations, the Ioffe mirror and the toroidal system, the toroidal system looks immensely simpler, and indeed it would have been [Laugh] if it had been stable. When you create a plasma by a big bang from a condenser bank you get the most appalling turbulence, which nobody could follow or understand, whereas with mirror machines you build a vacuum magnetic field which may be complicated, but it’s produced by coils that are bolted down to the floor. So, you’re starting from a very firm foundation instead of from something out of your control. So, although geometrically the torus looks simple, when you come to analyze it, the mirror machines are much simpler. I will admit there were skeptics who said, “No. This is not the way to go. It’s the torus, even though it is complicated.” And of course, in the long run they were right, but it was a long run before we got there.

Barth:

Do any skeptics come to mind?

Taylor:

Yes, Roy Bickerton, for example, was always skeptical. Bas Pease was not. He supported me, but he was also in love with the torus because he’d been one of the instigators of ZETA. There was undoubtedly a group that didn’t want to go this way but, in fact, the lab went that way. For a period all the effort was devoted to these mirror machines.

Barth:

For just a five-year period?

Taylor:

Yes, for about a five-year period.

Barth:

And what happened then with the rise of the Tokamak?

Taylor:

Then we come to the next step. Let me just see if there’s anything I’ve left out about the mirror machines? No, except to point out that John Adams had come from CERN, an accelerator establishment. Therefore he was very ready to accept the idea that theorists should say what’s going to happen, because that’s what you do in accelerators. You don’t make an accelerator and see if it works, which is rather what had happened on ZETA. Rather, you design it carefully, and then tune it. We were taking somewhat the same approach with mirror machines: you design the magnetic field and then you introduce the plasma. So, John was very welcoming of these ideas. And he also accepted theory as the dominant influence, because theory is the dominant influence when you design an accelerator.

Barth:

How then can we understand this switch back from mirror machines to toroidal machines?

Taylor:

Nothing lasts forever. Before I explain the switch I should say that as a sideline of the work on mirror machines we did a lot of mathematical work on adiabatic invariance in general. Unfortunately, much of this was not published. As I said, nothing lasts forever, and people began to realize that mirror machines were very nice as experiments, but actually they weren’t going to lead to fusion because of the collisional losses, which, notwithstanding the fact that we might have made the plasma stable, were still very significant. Gradually people began to move away from mirror machines because of these “collisional losses”. They began to realize that this was probably an insuperable problem. However, Dick Post never accepted this. He went on forever and ever.

Barth:

Even to today?

Taylor:

Certainly until he retired from Livermore. Adding more and more gizmos to mirror machines in the hope of overcoming this collisional loss, ending up with MFTF-B, the second version of the Mirror Fusion Test Facility.

Barth:

The last Livermore mirror machine?

Taylor:

Yes. They made a very large machine, which I think was never even switched on in the end. It was another of these machines that was canceled just as it was about to come to fruition. Dick never gave up the idea that one would overcome collisional losses, but most other people did. Amusingly, there was a friendly dispute about what one basic type of minimum-B should be called. Mike Larkin and I showed that one could make a basic magnetic well using only a single coil of wire, provided it had the correct shape. It’s just an academic thing, but it was very neat. This simple piece of wire creates a field that has all the properties of a typical magnetic well. From an engineering point of view it is not a practical way to do it, but as a mathematical toy it was very interesting. We discovered this at much the same time as Livermore, and there was a minor controversy over who was first and what it should be called. [Laugh] In Livermore they said that this wire looked like the seam on a baseball, and we said it looked like the seam on a tennis ball, which is, of course, the same shape. [Laughter] And so, there was a disagreement over whether it should be called the “tennis ball seam,” or the “baseball seam.” John Hiskes even wrote to Physics Today about this and about who had priority, I think he agreed that we did. [Laugh] But now I should turn to the swing back towards toroidal systems, where there are a couple of important developments.

Barth:

Could you please first explain why there was this swing back?

Taylor:

It is principally because people realized that these end losses or collisional losses were very likely to be insuperable. There was discussion about how big they are and whether they could be reduced. Various tricks were considered, notably by Dick Post and his collaborators, to try and reduce the losses, but no one was terribly convinced by them. My own feeling was that stopping up the collisional losses was beginning to look like making perpetual motion. Everybody knows it is impossible, but you might try to do it with a machine involving ball bearings rolling on a wheel. And then somebody shows that doesn’t work, so you add a few more wheels and make it more complicated. And it just gets more difficult to prove it doesn’t work. But you eventually become convinced that actually it doesn’t work no matter how complicated you make it. That was how I felt about stopping up these end losses. There were things you could keep adding like multiple mirrors, and putting on complicated electrostatic fields, but eventually you come to realize this was never going to work. So interest in the world generally, and certainly at Culham, began to swing back towards toroidal systems, “because in the long run they’re probably what we should have.”

Barth:

In the mid ‘60s you thought that the Stellarator could also be converted to an average minimum-B system?

Taylor:

I did, but that was just an aside. I wouldn’t count that as a major development. But I’d like to mention a spin-off from fusion, related to chaos theory. We are talking now about the 1960s when very little was known about chaos, but in plasma confinement one is naturally interested in where the field lines go. The question is, “If you follow a field line indefinitely, does it form a nice smooth surface?” or do small imperfections result in this structure being chaotically broken up? It is like the transition to chaos in a mechanical system, which later became a very popular subject. We did some very early work on this, because the magnetic field can be described mathematically in the same terms as one describes a Hamiltonian mechanical system. We certainly didn’t realize all the mathematical subtleties that lay behind it, on which many eminent mathematicians have made their careers since, but we did at least explore the idea of a transition to chaos in magnetic surfaces.

Barth:

Who is “we” exactly? Does it include Marshall Rosenbluth and Roald Sagdeev?

Taylor:

Rosenbluth, Sagdeev, Zaslavski and myself wrote one of the papers on the subject.^[2] I also introduced a simple model, which is now called the “Standard Map,” or sometimes the “Chirikov-Taylor Map,” because it was independently invented by Chirikov. I didn’t publish my version because it wasn’t in the direct line of my work. However, Tom Stix, who was a division head at Princeton and a world expert on plasma waves, publicized it. The first pictures I made of the Chirikov-Taylor map have since been reproduced many times, and appear in at least one textbook. I made the first picture on a Hewlett-Packard computer that looked like a typewriter. It only had three registers, x, y, and z, and you could transfer numbers from one to another and add them. This was really primitive computing, but it was the first desk machine to have a graphical output — a mechanically driven pen, like a ballpoint pen. Every time this primitive calculator calculated where the next point should be, the pen would go whir, whir, get to the point, plunk, and mark it. [Laugh] It did it at about that speed, about two points per second. [Laugh] I remember setting this machine to work and going off to lunch, leaving it running. [Laugh] When I came back, there was the first picture of the Chirikov-Taylor Map.

Barth:

This must have been quite an enlightening moment?

Taylor:

It was indeed.

Barth:

Could you see on the printout that it was uniform and didn’t lead to chaotic surfaces?

Taylor:

Well, you let it run for half an hour and you can see whether the points are generating a nice smooth surface or whether they’re going all over the place. It is very easy to see. That’s one of the attractions of the thing.

Barth:

How did the interaction with the other authors look like? This is the first paper you had with Culham?

Taylor:

No, the first paper I wrote on chaos was with Rosenbluth, Sagdeev and Zaslavski when we were at the summer school in Trieste.

Barth:

You were part of the Trieste Summer School in 1965?

Taylor:

Yes, the Trieste Summer School was a major event for a number of reasons. First of all, it brought together all the eminent people of the time. If you look at the list of participants it’s like a “Who’s Who” of plasma physicists. They all went to Trieste and we all worked together and a book was published, which for a few years was the bible of plasma physics. The School was so successful, because Trieste was a no man’s land in the Cold War; it was one of the few places the Russians and the West could visit and neither side have severe restrictions. There was also money available for what became the International Centre for Theoretical Physics, led by Abdus Salam. At that time the Centre didn’t have its own permanent buildings. I remember some of the lectures were given in a building that had once been the police station under Mussolini, and its main feature was that, being built by Mussolini, it was totally built with marble and the acoustics [Laugh] were diabolical. It was impossible to hear anything because of resonances and echoes. But it was fun and all very novel. Even going to the States to talk with the Americans had been a bit of a novelty. But to go where you could talk to the Russians, without their communist minder, that was absolutely new. (When Russians later came to visit me in Culham they had a minder with them.)

Barth:

Marshall Rosenbluth was there for, I think, nearly a year. How long did you stay at the Centre?

Taylor:

I was there for a few weeks. There was a very intense six weeks summer school, which led to the book.^[3] But then there was a continuing presence of plasma physicists at Trieste. Marshall was very much involved with that and went to Trieste several times.

Barth:

And there were also social interactions with the Russians?

Taylor:

Oh yes, of course.

Barth:

What did develop out of this meeting in Trieste for you professionally, in terms of new research ideas?

Taylor:

It is hard to remember that far back, and even nearer to the event it’s difficult to know what the influences were. My input was the work on magnetic wells, which I had only previously described at Culham. I described it at Trieste and it’s in the book. What I got from it was in particular some work on resistive instabilities, which Furth and Rosenbluth were involved in, and some fundamental mathematical work of Martin Kruskal (who I got to know well in later years). Looking back, Trieste was the best and most important cross fertilization event of the early years, and therefore probably of all time, because these things tend to get less effective as the program becomes more mature.

Barth:

Did you notice any particular difference in national styles of doing theoretical plasma physics? For example, if you compare your own style with Rosenbluth, or with Sagdeev and Galeev, do you see any difference? Would you be able to read a paper and detect a particular Russian style, for example?

Taylor:

Yes, I could tell you which is a Russian paper before I had read the first few paragraphs, without any trouble.

Barth:

Why is that?

Taylor:

First I should say that we were all very impressed by the standard of Russian theory, which I suspect in many ways was higher than in the West. This was apparently because fusion was important for the Soviet state. It all had to do with something Lenin said in the 1920s about “communism being the will of the people, plus electricity,” or something like that. Also fusion research was run by the Russian science academies, which have a very high standard. But the reason Russian papers are easy to recognize is that, as I used to say, “Russians don’t write papers: they write hints for the solution of the problem.” Russian papers are extremely condensed; they may contain everything but it takes time to dig it out, whereas Western papers tend to be more expansive and explain things. It may be that the Russians attribute to the reader a higher standard of knowledge than some of us had! So, it’s easy to tell a Russian paper: it’s very condensed and doesn’t explain everything. It assumes that you’re going to work it all out for yourself.

Barth:

Did you observe differences in style between American and British papers as well?

Taylor:

No, much less difference there. But to return to Culham. Interest is now turning back towards toroidal systems, but we still wanted to keep to the idea that we should start with a magnetic field that we can control and then add the plasma. So the toroidal machines that we first turned to at Culham were not the reversed field pinch. They were things like the Levitron, which has a conductor buried in the plasma. This is clearly no use for a reactor, but we argued that it was a very good device on which to do experiments on toroidal confinement. This machine was quite large and had a superconducting coil, which was very novel for its time.

Barth:

What was the major argument why it could never be converted into a reactor?

Taylor:

Principally because there’s a toroidal metal conductor buried inside the plasma, which has to be levitated. You can’t put it on mechanical supports because the plasma would strike these supports and either the supports would be destroyed or the plasma would. It was never a possibility for a reactor. In the experiment you support this central coil, which is superconducting, and then pull the supports away while you create the plasma and do the experiments. Of course the coil drops, so it’s a short-term experiment. It wasn’t all that successful, to be absolutely frank. There was also interest in the multi-pole, where you have several toroidal conductors, this time outside the plasma.

Barth:

How important was your role as an administrator to guide the building, funding, and budgeting of these various machines?

Taylor:

[Laugh] I certainly didn’t play much part in the budgeting. I could claim a role in the scientific program, but I wasn’t interested in management — except for recruitment, which I did take seriously and spent much time on. I did have a hand in office design though. Keith and I selected the new Theory Division location: the main point was it was to be near the library and quiet. I actually had measurements made of the acoustic transmission between offices in the Theory Division [Laugh]. So Culham had got back to thinking about toroidal experiments but not back onto the RFP line. ZETA still existed, despite being threatened many times with closure, but it was over at Harwell and run by a group of diehards. Nobody else was interested in it and it never moved to Culham, though that was partly because it was too big. Around this time there were two major theoretical developments associated with toroidal systems. One of these, by Keith Roberts and myself, was what we called “quasi-modes.” Theorists had always discussed perturbations and instabilities in terms of Fourier modes. Nobody had contemplated doing anything else. But Keith and I decided to do something else, and we showed that there was an alternative way of describing the perturbations in terms of what we called “quasi-modes,” which I also called a “twisted slice,” because it looks like a slice cut off a cake and then twisted. We found that it was very convenient to explain perturbations in terms of these quasi-modes, and we argued that when the perturbation grew to a large amplitude and nonlinear effects became dominant, it would adopt this form, not the Fourier form. Nobody took a great deal of notice then, but it turned out that twenty years later even the linear theory is best described in terms of quasi-modes and they became the cornerstone of Ballooning Theory. This was a really major development that Keith and I were within a hair’s breadth of discovering Ballooning Theory twenty years before it happened, but we overlooked the linear regime because we were seeking a non-linear solution. Another important development in theory was the Bootstrap Current. This was based on a discovery by Soviet scientists as part of research into Neoclassical Transport Theory. This theory was a big advance on what had gone before because it considered transport from the particle orbit viewpoint rather than in the Fluid Approximation, as hydrodynamicists do.

Barth:

Back to kinetics, essentially?

Taylor:

Yes, if you put in the orbits of the particles, it’s Kinetic Theory rather than Fluid Theory. In plasmas it’s known as Neoclassical Transport Theory, which was developed by the Russians, and also by Rosenbluth, Hinton and Hazeltine. One of the outcomes of Neoclassical Transport Theory is that there’s a toroidal current which arises spontaneously whenever there is a plasma pressure gradient. It’s one of these cross transport effects where a gradient in one quantity creates a flux of another quantity in an orthogonal direction. In Neoclassical Transport Theory it’s a toroidal current driven by a radial pressure gradient. This was regarded as an interesting anomaly, related to Onsager’s Relations in thermodynamics. However, in 1971 Roy Bickerton, Jack Connor, and myself looked at it again and discovered that it was possible for this current to build up and create a self-sustaining Tokamak, which we called the Bootstrap Tokamak.^[4] It wasn’t totally Bootstrap. It wouldn’t start up from nothing, but it could start up from a very small seed current. The idea that a mathematical curiosity could be a source of a real current of a few megamps was considered rather fanciful. But at least people were sufficiently interested to think they ought to look for the bootstrap current in their experiments. But they found nothing. I even went to a conference where someone from Oak Ridge said, “We’ve looked for this current. If it was even ten percent of what the theorists predict we would have seen it. So, there’s no Bootstrap Current.” So, for 15 years we agonized over why there was no Bootstrap Current when the theory said there should be. Then in 1986 Princeton held a press conference to announce that they had discovered this Bootstrap Current in their Tokamak Fusion Test Reactor (TFTR). When the announcement was made I went to see Mick Lomer, who was then the director of Culham. I didn’t get on very well with him and he didn’t get on very well with me, but I said, “Look Mick, Princeton has just announced they’ve discovered the Bootstrap Current. We can’t let them get away with it. We actually patented the Bootstrap Tokamak fifteen years ago.” He thought I was being facetious and said “Go away and do some integrals,” or whatever directors say when they want to get rid of their awkward staff. [Laugh] But later he called the PR Office and said, “Taylor’s just been in and said that we took out a patent fifteen years ago on the Bootstrap Tokamak. It’s all rubbish, isn’t it?” And they said, “No, we did have a patent on it.” [Laugh] So I went back and said, “Look, let’s get our lawyers to write to Princeton saying we’re going to sue them for infringement of our patent.” [Laugh] Unfortunately, when they investigated they found they had let the patent lapse. It was an amusing episode nonetheless. I’m pleased to say that planning for all modern experiments now includes an assessment of the Bootstrap Current. That took fifteen years to come to fruition. Another work, which was much more academic, was on two-dimensional plasmas. I got interested in this as an interesting bit of physics. It turns out that they have a number of very interesting features, which are counterintuitive. First of all, they can have negative temperature. That’s due to Onsager years ago, but the fact that you can have it in a two-dimensional plasma made people’s eyes pop a bit. Its only connection with fusion is that this two-dimensional system threw light on Bohm Diffusion, which we left a long time ago still unexplained. It turns out that Bohm Diffusion is an entirely natural consequence of a plasma having a two-dimensional character, as it does in a strong magnetic field. The third thing in this period, and by far and away the most important was the Theory of Relaxation. This goes back to ZETA again. When ZETA was operating it created a plasma in a very violent and uncontrolled fashion, which is highly unstable and a lot of turbulence ensues. When this turbulence died down the toroidal magnetic field at the edge of the plasma was in the opposite direction to what it had been when the experiment started. I can’t emphasize too strongly how remarkable that is, because you spend zillions of dollars to create a field in one direction, using massive copper coils, and the plasma reverses it. [Laugh] I should pay credit to Bas Pease at this point. He kept saying, “You theorists are no use. You can’t even explain why the plasma reverses the field in ZETA.” Nobody could argue with this, but ZETA had fallen out of favor, and although we were embarrassed we didn’t worry too much about it. But eventually Bas persuaded me to think about it again. That led to the Theory of Relaxation, which explains why the plasma field is reversed, and more importantly explains that the field is reversing as the plasma passes through its turbulent state into a lower energy stable state. This completely refutes what I said earlier, that you must start from a stable situation. Here you don’t do that. You let the plasma do exactly what it likes. You make no effort to influence it, but it falls into a stable state — and this stable state, in the case of ZETA, involves the reversed field. The reversed field is the signature of this “relaxation.” This created a lot of interest and was sometimes said to be responsible for maintaining the interest in reverse field pinches as distinct from Tokamak. It is probably the work that most people know me for, because it’s still mentioned and discussed even now.

Barth:

Did this show that reverse field pinches could still work well, because one could get rid of the turbulences?

Taylor:

Yes, that was indeed its implication. It turned out that the confinement in reversed field pinches still isn’t all that wonderful, but it is a lot better than we had thought. Another aspect is that the same concept of Relaxation explained many other systems in addition to the reversed field pinch, including the Spheromaks and Spherical Tori, and very complicated experiments in Los Alamos and UCLA where one plasma is injected into another, and it led to the whole field of Helicity Injection.

Barth:

Is it like a turbulent fluid that over time finds a stable position? Or how can we understand this? Is it like if you have a cup of coffee and you pour some milk in it that after a while it develops an equilibrium?

Taylor:

Well, it does have some similarities of that, but I wouldn’t describe it that way.

Barth:

It seems to violate the second law of thermodynamics, doesn’t it?

Taylor:

It does seem to be like that, which is why it’s so interesting. Let me put it this way. Think of the plasma as being a flexible wire, embedded in a viscous medium, through which you’re passing a large current, and suppose I were to ask “How would you calculate what configuration this flexible wire eventually adopts?” Because the wire is going to kink and wind itself up, and you couldn’t imagine following the motion. But you could find the final state by looking at the constraints on the motion of the wire, like its length, but also like the fact that its inductance times the current through it must stay fixed and then finding the lowest energy configuration that that wire can have subject to those constraints. It turns out, and you can do the calculation on the back of an envelope, that the wire goes to the state of highest inductance. I just applied exactly that reasoning to the plasma. What is the state of lowest energy subject to all the constraints on the motion of the plasma? Unlike a wire, the plasma has an infinity of constraints because the flux is trapped everywhere in the plasma, so it looks to be an impossible problem. However, it turns out that all the constraints can be expressed very succinctly in terms of what became known as the “Magnetic Helicity,” which is ∫A·B d³r in mathematical form and the calculation can be performed rather easily.

Barth:

Did the plasma relaxation work lead to the conservation of helicity?

Taylor:

No, it doesn’t lead to it. That the helicity is conserved is an input into the calculation. You know that it’s a property of the plasma, and you say, “Given that the helicity is conserved, what is the lowest energy state the plasma can achieve?” It will always lower its energy, but it cannot go any lower, because that would violate these constraints. It turns out that in a toroidal pinch this state has a reversed field. One then goes on to say, “What other forms of relaxed state might there be?” One finds, for example, that if one tries to pass more current, then the relaxed state changes its character. This second state had not been observed at the time I did the work, but Bodin later observed it in experiments on HBTX1A at Culham. That was a key point: when you predict something and somebody observes it they take notice. Precisely the same theory worked for the “Multi Pinch,” an experiment at General Atomics, which is again a torus but instead of having a circular cross section it has a figure-eight shaped cross section. The relaxed state can be calculated in such a shape, and it turns out to have remarkable properties, all of which were observed. It was quite impressive. There were important developments at Culham going on at the same time as the work I’ve been discussing. In a moment we’ll need to go back to that, but there is another theoretical development that was important, namely the Ballooning Transformation, which we alluded to earlier. This concerns toroidal plasmas, in particular Tokamaks, and illustrates the fact that in plasma confinement theory one needs to deal with a realistic configuration. Theorists may like to talk about infinite cylinders, even infinite media, but the engineers make things which are toroidal and often of a complicated cross-section. In most fields of physics, like hydrodynamics, for example, one can separate the properties of the medium from that of the configuration it is in. One can talk about the properties of water without worrying about the shape of the pipe, and then one can use those properties to discuss the behavior in a pipe of a certain shape. One can’t do that with plasmas; we should have made this point right at the beginning, because it’s fundamental to the whole subject. In plasma physics it is not possible to look at a bit of plasma and say, “It has certain properties. Now I will take those properties and calculate what the plasma will do in a particular machine.” That’s because, in a plasma, as someone succinctly put it, “Local effects have global properties.” An effect at one point propagates along the magnetic field throughout the system. There is really no such thing as a local property of a plasma. Its local behavior is affected by its global configuration. This is the big problem of plasma physics. It means, for example, that the loss rate of plasma in a cylinder is totally different from the loss rate in a torus, even if the toroidal curvature is small. This is a consequence of this long-range property. Each local bit of plasma “knows” that it’s actually in a torus and not in a cylinder. The importance of the Ballooning Transformation is that for the most important class of instabilities it overcomes this problem completely. If the wavelength of a perturbation is small, one can normally make an approximation, the WKB or Phase Integral approximation, based on the smallness of the wavelength relative to the size of the system. This is standard procedure and leads, for example, to ray theory in optics. You can’t simply do that with a toroidal plasma. Suppose you did set up a perturbation with a small wavelength at some point. Then this will propagate around the torus and return near this same point, where it will fail to match the assumed perturbation. Mathematically what this means is you can’t use the WKB Approximation. Well, we [Connor, Hastie, Taylor] invented the Ballooning Representation,^[5] which mathematically allows you to do precisely that. For the first time therefore we could discuss short wavelength perturbations in a realistic toroidal system. It’s just a mathematical trick, but it’s a clever trick. I received the Born medal from the German Physical Society for this work. (It’s called Ballooning because the instabilities balloon out like a puncture in a tire.) An interesting point about this development is that, as I mentioned earlier, these perturbations are precisely the sort that Keith and I had talked about twenty years earlier, when we invented the quasi-mode. But now I must go back to what was happening at Culham at the same time, because there were very important developments. If we go back towards the end of the 1960s I could say that Adams’ aim that Culham should have built an international reputation had been fulfilled and everything was going very well. Culham was a thriving establishment building several experiments and with a high reputation in theory. But then there was a very major setback. This appeared in the form of a government decision in 1967. At that time fusion research in Britain was at a level almost comparable with the United States. It wasn’t as big as in the States, but it was in the same league, and therefore did appear perhaps anomalously large for a country with Britain’s resources. Then the government announced that fusion research in the UK should be reduced to about half what it had been previously. This, obviously, was a severe blow to Culham, particularly as it was scientifically doing so well.

Barth:

Was Adams still the director at that time?

Taylor:

Adams was still director, yes.

Barth:

Why was he not able to deflect this decision?

Taylor:

I’m coming to that. This announcement was the result of a recommendation by a review committee chaired by James Lighthill. This took place at a time when Culham director John Adams had recently been appointed as senior scientific advisor in the new Ministry of Technology. The Ministry’s job was to foster technology in British industry, and the Prime Minister, Harold Wilson, declared that “The future of Britain lies in the great white heat of technology.” I’m sorry to say I think this appointment at the MinTech (which much reduced the time John could devote to the lab) distracted him from what was happening in fusion. I’m a tremendous admirer of John Adams. I think he did a wonderful job in establishing Culham, but I also think, and I’m not going to say more, that because he was spending a major part of his time on this important job as the chief scientist in the Ministry of Technology, that he took his eye off the ball. I suspect he didn’t really take the Lighthill committee as seriously as he should have done. The committee interviewed all the division heads, including myself in a rather minor capacity. They made it clear that they thought we were all doing brilliant work scientifically, but their view was that there was no economic future for fusion, and therefore it should be cut back.

Barth:

How was the response at the lab? Were the scientists disillusioned? Were they angry? Were they leaving for other positions in the area?

Taylor:

Not immediately. It was a shock. I can’t deny that. But somehow, I suppose, we believed that it wouldn’t actually happen. The government had said it was going to happen, but it wouldn’t be the first time governments have said things are going to happen and they didn’t. We were doing so well. It was one of the most famous fusion labs in the world. How could the government possibly cut this in half? The decision was toned down slightly to say that the cut would be ten percent a year for five years. What actually happened was that the first ten percent reduction was made by cutting the fat and delaying things a bit, and didn’t really do much harm. The second ten percent reduction was made by hiving off bits of Culham to other projects, or budgets. [Laugh] In particular, Culham hived off something called the Astrophysics Unit. I haven’t mentioned it before because I played no part in it, but alongside the fusion work there was some astrophysical plasma work at Culham. And so a ten percent reduction was achieved by hiving off this work to the Science Research Council, which was responsible for basic research in Britain. By the third year the powers-that-be relented a bit and another review committee, chaired by Sir Harold Massey, recommended that work should continue at the level we had then reached. It may well be that this just reflected the fact that the first committee was chaired by Lighthill, who was not very sympathetic to Adams and Culham, whereas the second committee was chaired by Massey who was much more sympathetic.

Barth:

Do you know why Massey was more sympathetic to Adams and Culham than Lighthill?

Taylor:

No. I didn’t know Lighthill enough to comment on that. I’ve understood it in the terms that Adams really didn’t take this committee seriously enough. The committee was certainly not against Culham on any scientific grounds, and indeed it’s precisely at this time that I got elected to the Royal Society for my work, and I believe that Lighthill may even have been one of my sponsors. He just said “We understand all the wonderful science that’s being done at Culham, but we’re here to assess the economic future [of fusion] and we don’t think it’s all that great.”

Barth:

This was the situation in the late ‘60s?

Taylor:

The committee made its report in 1967.

Barth:

And this laid the groundwork for budget troubles in the 1970s?

Taylor:

We had to reduce the budget, but there was a more lasting effect because it brought in the concept of “diversification.” This started to be very fashionable in the Atomic Energy Authority generally, and, after the cut-back, at Culham. The idea of “diversification” was that Government Labs should sell their expertise to whatever branch of industry would pay for it. Our sister establishment at Harwell went completely over to this concept. It virtually ceased to be a government research establishment and became much more like a business park with lots of spin-offs from its Atomic Energy research, but which had actually nothing to do with Atomic Energy.

Barth:

Like nuclear clean-up companies?

Taylor:

Nuclear clean-up, of course, has a lot to do with atomic energy. I refer to things further removed than that. I can’t remember what they were at Harwell but it is now a thriving business park. There was strong pressure for Culham to go down that same route. There was a good deal of anguish about this, particularly on my part, I’m afraid, because I felt that resources that should be used for fusion were being “milked” to support diversification. Examples of diversification were the use of Culham’s laser expertise for industrial projects, including something I used to joke about, cutting out the leather seats on Rover cars. [Laugh] Also, because of its fusion work, Culham had a great deal of expertise in high voltage research; consequently a high voltage test facility was set up, which did lightning strike tests on aircraft and things like that. This diversification meant that Culham ceased to be solely a fusion and plasma physics laboratory. In fact fusion is now less than half of the activity on the whole site.

Barth:

I take it from your comments that you were concerned about this development?

Taylor:

I was very concerned about this. I didn’t really like it, to be quite honest.

Barth:

Can you expand on this point? Why were you concerned? Is it a basic science vs. applied science tension?

Taylor:

Yes, partly. I always thought the work we were doing was interesting, exciting, and important because it sat on this border between pure science and applied science. When I was doing weapons work the attraction was that it involved very basic science but had a practical, some would say an unfortunate, application. I felt much the same about Fusion (even if it was a long way from practicality). I thought that that was the role of a government lab. On the other hand I felt using lasers to cut-out parts for cars, or testing nose-cones of aircraft, was a job for industry. In my world there were the universities where you did academic research, there was industry where you did things with immediate application, and there were government labs, which occupied the ground in between. But this wasn’t a “politically correct” attitude. It was the beginning of my falling out with Culham leading me to eventually leave it. Another very significant development that began at this time was that in order to defend the fusion part of our activities, this began to be more and more involved with Europe, and the Euratom Organization. So Culham began to diversify; became more closely associated with Euratom; and cut back on its fusion research.

Barth:

Were you the driving force among the critics of this change? Were there other critics who stand out? How would you describe the tension in the lab about the general policy direction?

Taylor:

Oh, first there was yet another development I’ve forgotten. Shortly after the committee recommended the reduction in effort, John Adams left Culham and soon went back to CERN, and Bas Pease became Culham’s director. So it was a pretty turbulent time all around. Thus it was Bas Pease who had to deal with the situation I’ve just described. It was Bas’ decision to defend fusion by becoming more and more integrated with Euratom. (Remember, Britain was not then in the European Community.) The idea was, to put it very bluntly, if we were sufficiently tied up with Euratom the UK government couldn’t cut us anymore because Euratom would object.

Barth:

That is, Culham’s Euratom connection can be regarded as a “safety line”?

Taylor:

A safety line, yes. Anyway, these were the developments, and Bas was responsible for putting them into practice. I didn’t like most of them, but I was just one person. The alignment of Culham’s fusion research with Euratom, eventually led to JET many years later.

Barth:

It seems then that JET is the outcome of a particular development that led Culham away from the basic fusion effort it had before?

Taylor:

I think that in a sense this is true. Another factor was that Culham had been thinking about building a very large toroidal experiment before the JET experiment was proposed. I suppose you could trace the origin of JET all the way back to this period. But I have, in fact, overlooked a very important development: during this period the Tokamak had arrived. What had happened was that the Russians had pursued their own way with Tokamaks, which nobody in the West had adopted. The West had reversed field pinches and Stellarators, which are both toroidal devices, but they didn’t have the Tokamak (Tokamak is a Russian name, meaning “toroidal magnetic chamber.”^[6]) The Russians had pursued their own line with the Tokamak and suddenly announced that they had achieved amazing results with it, which few initially believed. Bas Pease arranged that in early 1969 some of the experimentalists from Culham should take their laser diagnostics to Moscow. There they would fit them onto the Moscow Tokamak and check whether the Russian results were correct. (At that time the Russians didn’t have sophisticated laser diagnostic measurements of the temperature, which was the point at issue.) Derek Robinson and Nick Peacock shipped their apparatus to Moscow and spent, I think, about six months there. This was a very important event and possibly Bas Pease’s greatest claim to fame is that he negotiated it. Remember, we’re still in the Cold War, but he arranged to ship scientific apparatus that might have been for anything that Russian security wished to think it was, to Moscow. The people who went to Moscow came back with all sorts of tales about what went on [Laugh] in Russia. It was a distinct coup, and it showed that the Russians were right. The Tokamak had achieved much higher temperatures than anybody else, so there was a mad scramble to convert all experiments to Tokamaks. Princeton even converted its Stellarator into a Tokamak, which was an amazing turnaround. Everybody rushed to get Tokamaks, all as a result of Culham having confirmed the measurements that the Russians had claimed on their Tokamak. Since then it’s been Tokamaks all the way.

Barth:

Did this lead to groups of scientists getting out of the field because they were disappointed that their machine didn’t make it? Was there any kind of tension after this move towards the Tokamak, or did scientists accept the Tokamak as the most successful machine?

Taylor:

I think most people accepted that it was the most successful machine. But the concentration on Tokamaks was certainly not popular with those who were forced to close their own experiments to release funds, like Hugh Bodin. That was something I was very annoyed about, partly because I was associated with the experiments, but also because, e.g. when JET was set-up, we were assured that this would not happen. The 1980s were dominated by the impending presence of JET. The design team for JET, led by Paul Rebut, came to Culham, but they were only the design team. No decision even to build it had been made. A number of Culham staff joined the design team and they designed JET at Culham. Then came the big question: “Where is it going to be built?” The usual procedure was followed: several countries put forward proposals that it should be built in their respective countries, and a committee was formed to go around and view the sites and decree which was suitable. In the end it came down to either in Germany or Britain. There didn’t seem to be any way of breaking the impasse: both were considered good sites and capable of hosting JET. But then there was this famous hijacking at Mogadishu. In 1977 a German aircraft was hijacked at Mogadishu and the passengers were rescued by a team of British special agents.

Barth:

I remember this differently, that the Germans had Special Forces at this time, the GSG-9.^[7]

Taylor:

I’m afraid I don’t recall the details, but the German government ended up being extremely grateful for the help that Britain had given them. In recognition of this they agreed to have JET at Culham. In fact the British government was desperate to get JET, because they wanted to have a European Project on British soil, and were willing to make all sorts of compromises to get it. For instance, one of the issues was that there was no international school in Britain; the foreign contingent wanted one, and in no time a school was set up on the road to Abingdon [near Culham] as part of the deal to have JET. So JET came to Culham. What worried me was that it would drain resources from Culham, to the detriment of other work. Palombo, who was then head of Euratom, said to me, “No, Bryan, it’s all right. We shall see that there is not too much drain on Culham’s resources” because, as he put it, “JET is a Euratom project and we want it to be seen to be a Euratom project.” But, of course, what I expected to happen did happen. Whatever Palombo might have wished, it’s infinitely easier for a physicist at Culham, who only has to walk a hundred yards, to join JET. This does not disrupt his life, his family, his children’s schooling, his car, his house. On the other hand, a matching physicist from Garching (Germany) has to drag his family, change his children’s schools, and all the rest of it. So, there was a much greater drain on Culham’s staff than Palombo suggested. I was a bit annoyed about that, because I didn’t want to see Culham drained. So, I was against JET. Not on any scientific grounds, but because it was doing damage to Culham.

Barth:

Did other theoreticians or division heads share your point of view?

Taylor:

No. I didn’t get much support for this view, I’m afraid. By the mid 1980s I felt that Culham was no longer the congenial place that I had found it for the last twenty years, and I decided I would leave. But before we just come to that, there was another aspect of the interface between JET and Culham, connected with what I’ve just said: British staff at JET were in an anomalous position. They were not employed by JET. Everybody else, the Germans, the French, the Spaniards, etc. were JET employees. People who came from Culham were not — and they still received British salaries.

Barth:

Which were lower than the other salaries?

Taylor:

Which were lower than the Euratom salaries, by a large factor.

Barth:

This then led to a two-tier society?

Taylor:

There was a two-tier society in JET, the British being, in their eyes, greatly disadvantaged. (There was also another difference between the contractual position of the British working on JET and the JET staff. This concerned their terms of employment after JET was finished, because JET was supposed to be a finite life undertaking.) As a result the British staff agitated all the time to get better terms, and they eventually went to the European court. They mounted a legal challenge to the British government saying that the terms on which they worked at JET were “discriminatory.” The argument went on at a very high legal level for a very long time, but eventually the European Court somewhat ruled in favor of the British staff in that they should have better terms, but they didn’t go all the way and say they should have Euratom terms.^[8] A compromise was reached whereby they would stay on the terms of employment that British staff had in the rest of Culham, but they would get an enhancement of their salaries to bring them nearer to the Euratom staff. But it didn’t decree that they would become Euratom staff, which is what they originally wanted. (This created a three-tier society; Euratom/JET staff, UK/JET staff, and UK/Culham staff.) The result of all this was that the Culham staff working at JET had no real connection with Culham. There was very much an “us” and “them” attitude. I thought it was unfair that people given the opportunity to work on this highly prestigious experiment JET, where they will get all the glory and publicity, should also be given higher salaries. I thought it was those left behind in Culham, who had severe budget problems, some of them even losing their jobs because their experiments have been cancelled, who should be compensated by bonuses, not the people who went to JET. [Laugh] But, of course, I got nowhere with this argument. I became alienated from the Culham management and was eventually dismissed from the Management Committee but I took on the title of Chief Physicist, which in many ways was a very privileged position. I was free of managerial responsibility, but I could do whatever research I liked. Although I enjoyed this situation, I felt that I had spent too much of my life in the UKAEA and Culham (in fact 34 years) and in 1989 I resigned from Culham and went as Professor of Plasma Physics to The University of Texas in Austin. Texas was a new experience. Of course, I had given many individual lectures, but this was the first time I gave a course of lectures. In fact I had a light load. I gave the ‘Special Topics in Plasma Physics’ course for two years and continued my individual research in the Institute for Fusion Studies. Despite my reservations about embarking on a university career some 35 years earlier, I found I thoroughly enjoyed my time at UT. I returned to England in 1994, intending to retire, but in fact continued active research as a consultant to Culham Laboratory up to the present time (2007). I think we’ve now covered everything except possibly the Scaling Laws. When fusion got to the stage of large machines, theory had somewhat diminished in importance relative to experiment. The way that experiments mostly proceeded was by empirical scaling laws. One simply took the data, made a good fit to it and extrapolated to the next machine in order to estimate its performance. I never felt that was a very satisfactory way to proceed, and one day I hit upon the idea that if one took any basic model of the plasma, be it conducting fluid, guiding center, gyrokinetic or a fully kinetic particle model, then the relevant equations are invariant under certain transformations. Consequently, without solving any transport problem, any scaling law based on that model must similarly be invariant. This constrains the form that the scaling law can have. Jack Connor and I worked this out in detail and could then say to the experimenters, “Go back to your empirical scaling laws and see which, if any, of these sets of constraints are satisfied by your empirical laws and this will show which underlying plasma model is appropriate. Alternatively, take a model of the plasma and make sure the empirical law you use satisfies the constraints of that model. Such laws are now sometimes called “Constrained Scaling Laws,” or “Physical Scaling Laws,” and are more in the spirit of true physics than the empirical laws.

Barth:

Could we come back to your interactions with Princeton scientists like Ed Freeman, or Lyman Spitzer?

Taylor:

My first introduction to the subject involved Lyman Spitzer, because, as I said earlier, I went to a meeting at Harwell where he was one of the main speakers. I saw him several times when I visited Princeton, and I wrote to him a few times about various problems, but I couldn’t claim we had a very close association. My interactions were more with Ed Frieman and members of the theory group such as Carl Oberman and John Johnson, or the mathematician-cum-plasma physicist, Martin Kruskal. Ed was head of the Theory Group at Princeton during its glory days and during the period that Culham was trying to catch up to them. I never actually worked at Princeton PPL for a lengthy period, but I made many visits for periods of a few weeks or so, and always felt very much ‘at home’ there. I did, however, spend two lengthy periods in Princeton at the Institute for Advanced Study. As everyone knows, this was Einstein’s Institute. It’s a very interesting place; very academic, in many ways exactly like a university, but in other ways different. The professors are not obliged to give lectures and there are no undergraduates. My contact with it came through Marshall Rosenbluth, who had moved to IAS, after working at General Atomics for many years, where I visited him many times. Marshall and I knew each other very well, and when he went to the Institute for Advanced Study he invited me to go there. The institute has a tradition of inviting experienced people, who are not permanent staff but are, in some sense, “faculty,” who come for periods of anything from a year to a few years. There are also post-doc students who come for a few months to three years. I took a year off from Culham and went to the Institute in 1969. I enjoyed the IAS very much but with occasional misgivings. At the Institute one is free to do as one wishes, and doesn’t have to bother with students. On the other hand it is somewhat an ivory tower. I spent most of my time with Marshall and both of us made frequent visits to PPPL, a short distance up the road from IAS.

Barth:

Did you develop new scientific ideas during your time at the Institute for Advanced Study?

Taylor:

To be honest, no. I can’t say that any of my best work was done while I was at the Institute. I certainly enjoyed it, and the experience was very valuable. I have said I wish I’d taken a permanent job at the Institute, but on the whole I think it was wise that I didn’t because I’m not sure I would have fitted in. It’s a rather rarified atmosphere.

Barth:

You are a first-rate theoretician. What else would it take to fit in at the Institute?

Taylor:

Perhaps I would have to be more rarified or more first-class. I mean, I know my limits. I’m not in the category of Freeman Dyson, for example, who was the leading physicist there. I enjoyed talking to Dyson and got on well with him, and with John Bahcall, the famous astrophysicist, who was largely responsible for sorting out neutrinos from the sun. But I hardly met anyone else, I’m afraid, and I think that was true of Marshall to some extent as well. I like to think I’m a good physicist, but to some extent I’m a bit of an amateur. [Laugh] I’m not truly an intellectual. So I don’t think I would have fitted in long-term, but I very much enjoyed going as a visitor. I went to IAS in 1969, 1973 and again in 1980. The last visit is an interesting story. At the time there was talk about founding an Institute for Fusion Studies, and the DOE called for Proposals. Marshall would have liked to have had a bid from the IAS for the new Fusion Institute, but the IAS felt (rightly) that it didn’t fall within their interests. Marshall therefore persuaded the University of Maryland, where I think Chuan Sheng Liu was involved; to agree to make a joint proposal in which Marshall would lead a section of the Fusion Institute at the IAS, but the main body would be at Maryland. Marshall called me and invited me to join in this bid as part of his section at IAS. I’m a sucker for flattery, so I said, “Yes, I’d love to join your institute, Marshall.” So I was set to be offered a long-term position at the IAS, but contingent on this proposal between Maryland and Marshall being successful. I started negotiating with the Institute about my salary, and more importantly about housing. (It was the custom for long-term members of the IAS to be offered houses owned by the Institute.) So I was fairly deeply in discussions with IAS when Marshall called me over the Christmas holiday and said, “I’ve changed my mind. I’m going to Texas.” [Laugh] And though Marshall and I were great friends I can’t deny that I was a bit miffed by this. It was a complete turnaround: we had been discussing going to IAS, then he suddenly rings me up to say, “I’ve dropped out of the Maryland/IAS proposal. I’m going to Texas. I’m putting my name as the head of their proposal.” Of course, they eventually won the bidding and so the Institute for Fusion Studies was born in Austin Texas.

Barth:

Leaving you in the cold?

Taylor:

Leaving me in the cold. Marshall went on to say, “You’ll come to Texas as well, won’t you?” But I said, “Well no, one of the attractions was coming to IAS, which is a very prestigious institute where I’d be next door to Dyson and Bahcall and feeling that I was a great man. I won’t feel like that in Texas. I’m sorry Marshall but I’m committed to IAS in Princeton.” I wrote to the then director of IAS and said, “You offered me a job. I admit it was contingent on the proposal, but I was really looking forward to coming. Marshall has now backed out, but I would still like to come to IAS if you would have me. I think I can arrange to keep my salary from Culham, so actually you would only be giving me facilities. Would you still let me come?” He agreed, and so I went again to IAS (in 1980-81). I was largely on my own there, but I worked a bit with John Bahcall, and, of course, I visited PPPL. I really regarded it as a bit of a break and a nice place to be. They make one extremely welcome at IAS.

Barth:

Could you tell us about your collaboration with Jack Connor and Jim Hastie?

Taylor:

I worked with both of them, actually since the beginning of Culham.

Barth:

How did this look like? Writing a paper with three individual theoreticians is a complex interaction. Could you describe this?

Taylor:

Most physicists now write joint papers, and single-author-papers are getting rare. I’ve written many single author papers myself; but a good proportion of the other work has been done with Jack and/or Jim, usually with both of them. So, what was it like? Well, it was like Topsy, it just grew. There was no sudden starting point. Jim Hastie had been recruited just before I took over Theory Division, but I think I was in charge by the time he came into his post. The first work I suggested for him was to extend the work I had started on magnetic wells and confinement in mirror-cusp fields. I had discussed the principle, the confinement, and the stability of magnetic wells but hadn’t determined the maximum plasma pressure you could have in a magnetic well. Jim and I did that calculation jointly, in fact Jim may have done more of the work, but I wrote the paper. That’s just because I feel I am better at writing papers than Jim.

Barth:

In what sense?

Taylor:

I think most people agree that my papers are easy to understand — perhaps too easy! I know we got on very well together. Jim is extremely persistent when it comes to complicated algebra, which I was never all that keen on. I don’t have the stamina. Whereas I would blanch at the sight of two or three pages of densely-written formula, Jim wouldn’t be bothered by it at all. So, it was a very good collaboration. I tend to be very intuitive, and feel I know the answer to a problem before I calculate anything, and Jim would do it through the complicated mathematics. We complimented each other.

Barth:

How about Jack Connor?

Taylor:

I don’t quite know how I got involved with Jack but I did recruit him. I remember interviewing him and saying at the interview board that “We may have interviewed today the man who is going to be my successor.” And now he is my successor as head of Theory Division. The first joint work I recall with Jack (and Roy Bickerton) was on the Bootstrap Tokamak in 1971.^[9] But I think our collaboration began in earnest in 1977 with “Scaling Laws for Plasma Confinement.”^[10] I had this mad idea, that, using what I hoped would turn out to be related to Renormalization, we ought to be able to work out the scaling law, say for confinement time, for any basic plasma model without having to go through a detailed Transport Theory. We ought to be able to do it just from the fact that if the basic equations were subject to a certain transformation then the confinement time must be amenable to precisely the same transformation. I remember going to Jack and saying, “I’d like to work all this out. How about you helping me to do it?” Jack did so and we wrote the paper. Probably because of that collaboration, I later always naturally went to Jack with anything I thought of. The next important collaboration began with a paper I presented at Berchtesgaden (“Does Magnetic Shear Stabilize Drift Waves?”).^[11] That was an important turning point because it had been said that “magnetic shear,” (the fact that the magnetic field at different levels in the plasma is in different directions), would stabilize a disturbance called the “drift wave.” There were calculations to support this, but they were in a very elementary model, which didn’t take into account that the real system was toroidal. (I mentioned earlier that this is something that it’s always dangerous to do, because plasma always “knows” what configuration it is in.) I was having difficulty understanding the plane slab calculations, which are rather complex. I could see that because of the shear, the drift wave begins to radiate, and this damps out the oscillation. That was my interpretation, at least, and I began to worry about the extent to which that would still be true for a toroidal plasma. I then thought of a great analogy from radio antennas. A single dipole radiates in all directions, but if you put other dipoles in front of it then, depending on whether they are slightly longer or slightly shorter than the primary dipole, they can enhance or suppress the radiation. This is the principle of the Yagi Antenna Array, which I knew from my days in the Air Force. It occurred to me that if a drift wave on one plasma surface loses its energy by radiation, then perhaps another drift wave on a nearby, slightly different, surface could suppress the radiation. I could see that this wasn’t important in the plane slab, but it could become important in a torus because that introduces a small difference between one plasma level and another. I did the calculation and presented it at Berchtesgaden but using a very crude model and not a rigorous calculation. Later I went to Jack and Jim and asked “Could we do a rigorous realistic theory?” It turned out, largely thanks to Jim and Jack’s efforts, that one could do an extremely elegant theory, now known as the Ballooning Theory, for which we’re now famous! We were all delighted to see how elegant it actually became: it turns out to be mathematically just beautiful. The problem is defined by a complicated, difficult-to-solve, two-dimensional partial differential equation. We discovered that for the important short wave length oscillations, “high-n” as they’re called, you can split this two-dimensional problem into two separate, almost trivial-to-solve, one-dimensional equations. The step from a two-dimensional partial equation, to two simple one-dimensional equations, was a tremendous advance which none of us quite expected. It was just a delightful piece of good fortune that the mathematics turned out to be so elegant, simple, and correct. It’s the sort of calculation which, when you show it to another physicist or mathematician, they instantly see that it must be right. It’s just “sweet,” as Oppenheimer said in a very different context. Again, I think I wrote the paper, but of course, they tore my drafts to pieces and changed it. In later years I joked that whenever we wrote a joint paper there was always an episode where Jack went through it putting commas in, and then I went through it taking them out again. [Laugh] It was always a very genuine collaboration. You do read of cases where one of the collaborators in a joint paper didn’t do much. Our collaboration was never like that; any one of us could have written the paper, but I usually ended up with the job because I rather like writing papers and they were quite happy for me to do it. And seemed to think I did a good job.