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Bogdan MAGLICH
Migma Fusion
Migmacell --- A Low-Gain "Driven" Fusion Power Amplifier As An Interim Energy Source
Bogdan C. Maglich
Migma Institute of High Energy Fusion
Fusion Energy Corporation, Princeton NJ
( Talk given at The International Workshop on Emerging Concepts in Advanced Nuclear System Analysis ~ March 29-31, 1978, Graz, Austria; This is an expanded version of the invited paper presented at the Electric Power Research Institute Review Meeting on Advanced Fuel Fusion, June 27-28, 1977, Commonwealth Edison, Chicago; To appear in Nuclear Instruments and Methods, April-May 1978 )
[ Appendixes ]
Abstract ~
A fusion program less ambitious in its objectives and technology than the official programs, but such that could be reduced to practice before the large "ignited" plasma fusion power reactors with "infinite gain" become a reality, is described. "Migmacell" is designed as a "driven" power amplifier, energized by fusion, with a gain of 1.5 to 3. By recirculating a significant fraction of the output power, migmacell is a small (1 m. in diam.), self-sustained power source of 100 KW to 5 MW. By using direct nuclear collisions in "self-colliding orbits", it operates at the equivalent kinetic "temperatures" at least 100 times higher than thermonuclear devices. From the point of view of plasma physics, migmacell is a simple "colliding-beam" mirror with large gyroradius, highly non-adiabatic orbits and highly non-isotopic density peaked at the center. Focusing action results in low classical end-losses compared to plasma mirrors. The fusion power density is high, 0.1 KW/cm3. Diamagnetic effects are confined mostly to the central region.
High-energy migma fusion renders it possible to utilize the environmentally acceptable "advanced fuels" such as D, He3 or Boron, rather than D-T, thus lending itself to a "clean fusion" power source, which is neutron-free or neutron-deficient. Larger plants are envisioned as a plurality of standardized migmacells, thus solving many problems in power transmission and distribution.
Three stages of the program are completed. The experimentally achieved collision energy of ~ 1 MeV (equivalent kinetic "temperature" of 10 10 degrees K) and the energy confinement time of (2.21 + 0.05) seconds are sufficient for an advanced-fuel fusion reactor, but the central density of (2.2 + 0.7) x 10 d+/cm3, limited by the vacuum and the injection rate, is low. The colliding beam luminosity (rate per o = 1) is L = 1027 cm-2 s-1. Apparatus for Stage 4 (1 year program) whose aim is to achieve a large density regime, has been assembled and tested. Economic projections indicate a competitive power source. State-of-the-art technology is assumed throughout.
1. Introduction ~
1.1 ~ Problems Associated with Fusion Reactor Concepts of the Official Government Programs
It has been generally assumed that the "ignited" fusion power reactors, using Tritium-Deuterium and Lithium as fuel, whose power gain ration is theoretically infinite, will be the ultimate source of energy. It is also believed that they will become an engineering and economic reality only in the next century. Their scientific feasibility has not yet been proven. There are a number of experimental difficulties, some expected and understood, some not (Ref. 1-3). The concept of inductive toroidal heating has been substituted by the neutral beam injection into tepid plasma.
It has been pointed out recently that, if and when the planned ignited reactors work, they may not be acceptable to their ultimate users, the electric power industry (Ref. 4-6). This is, firstly, because of their use of the radioactive tritium as fuel: the tritium-deuterium-lithium fuel cycle planned for plasma fusion reactors could result in the radioactive waste problems comparable to those of the fission reactors; the second problem is their large size, high cost and long lead time (Ref. 7-11). For example, the projected size of the ignited fusion reactor UNMAK-1 is comparable to the Great Pyramid of Cheops (Ref. 12).
Additional difficulties with the T-D-Li fusion reactors arise from their high neutron flux which can be used to breed plutonium, thus opening a new nuclear proliferation problem. It has become known that the USSR has temporarily abandoned Tokomak as a fusion power source. Soviet Tokomaks are being developed now as neutron sources for the hybrid fusion-fission satellite reactor (Ref. 14).
There are also problems associated with the fuel supply for fusion reactors. Today, tritium is being produced in the fission reactors. This implies that the first generation fusion reactors may depend on uranium for fuel. The world’s supply of lithium may also be limited.
1.2 ~ What are the Aims of the Migma Program?
The Migma Program of Controlled Fusion is a less ambitious fusion program than that of the US, Soviet or other governments, but such that could be implemented before the ultimate answer to the world’s energy needs --- the ignited fusion power reactors --- become a reality. The elemental fusion power cell of the Migma Program, the migmacell, can be considered a "power amplifier using fusion" rather than a fusion power reactor. It is designed to output only 1.5 to 3 times as much energy as put in. In spite of this low gain, the energy output exceeds the input. Thus, a part of the output energy can be fed back into the input and the energy generating process will be self-sustained.
The migmacell differs conceptually from other energy systems in that is not an "ignited", but a "driven" energy generator.
All energy systems used today, once ignited, are sustained by feeding into them only one ingredient, fuel, whether fossil or nuclear.
A possible exception is the automobile, where a small fraction of newly generated power goes back into the cylinder to provide the spark. However, the spark energy is negligible compared to the energy released in internal combustion. Therefore, an internal combustion engine, too, is an "ignited" system; it operates almost entirely by the addition of fuel.
Ignited systems are fuel-intensive. Their energy gain is "infinite" since zero (or very little) of the system’s energy is fed back into the system.
In contrast, both fuel and energy must be fed into the migmacell. This input of fuel and a significant amount of energy produce, say, three times as much energy out; in turn, one-third of that output energy is fed back into the input of the cell. The energy gain in the migmacell is, then, 3:1. This is considerably smaller gain than that of all other energy machines today. This is why the migmacell is called a driven energy source, or a "power amplifier", to differentiate it from a fusion reactor.
The idea of a power amplifier (as opposed to a power reactor) has been proposed and discussed by others in the past (Ref. 78). The Migma Program is the first experimental program aimed at achieving it.
The essence of the approach of Fusion Energy Corporation is its belief that, if the aims (in terms of energy gains) for a fusion engine can be reduced, controlled fusion can become a reality sooner. Our view is that the official fusion programs have not produced energy after 25 years of research because they are aiming too high: at "ignited" systems with "infinite" energy gain. Our position is that the higher energy input, the more likely the controlled fusion system will work; and that the presently pursued plasma fusion devices are "under-capitalized" in terms of energy invested.
Since the migma fusion process is initiated by direct nuclear collisions in intersecting orbits (a modified concept of "colliding beams") rather than by the heating of plasmas, it does not have to use the uranium-tritium-deuterium-lithium cycle. If migmacell works, it will utilize "advanced fuels" such as non-radioactive deuterium, helium-3 or boron which will provide environmentally clean, non-radioactive, non-polluting, neutron-free (or neutron-deficient) power source with a minimal waste heat released to the environment. It is the view of at least some projectionists to the utility industry that only the advanced fuel fusion reactors may be acceptable to the industry, and that advanced fuel fusion research should have a parallel rather than a follow-on role (Ref. 4-6, 15).
Our detailed scientific and engineering projections (Ref. 16) show that, if our theoretical expectations are correct, a demonstration power cell can be built 5 years from the completion of the "critical tests" of Stage 4. Stage 4 is a one-year program.
1.3 ~ Physics is a Living Science
Controlled fusion is considered to be still very far away only because most of the fusion programs have been, for historical reasons, based on the attempts to almost literally "tame the H-bomb". If you started working on fusion today, you would do it differently from the way it was started 25 years ago. Controlled fusion will not necessarily emerge from Plasma Physics.
Physics is a living science. Every decade brings a number of new ideas and concepts in physics. An example is the development of the laser technology (Ref. 17) of the 1970s, developed in High Energy Particle Physics, is another example.
The Migma Program uses mostly the concepts and technologies of the 1970s, rather than those of the 1950s.
1.4 ~ Concepts and Technologies of the Migma Program
Migmacell uses a combination of 17 ideas, concepts, and inventions (Ref. 18, 19), many of them borrowed from operational devices. These are:
(1) colliding beams
(2) self-colliding orbits (Ref. 10-22)
(3) weak focusing (App. A4 of this paper and Sect. 4 of Ref. 23)
(4) synthetic plasma --- electron-impregnated migma or "eligma"
(Sect. 2.4)
(5) plugged migmacell (App. A6)
(6) linear conversion of MeV ions into electric energy by
deceleration (App. A6)
(7) highly localized central trapping of MeV ions (Ref. 24)
(8) incoherent cyclotron RF signal (Ref. 25; see also Ref 23,
24)
(9) energy-coincidence ("fast-slow" coincidence) of charged
fusion products (Ref. 26)
(10) magnetron-type "solid body rotation" of the electron space
charge (Ref. 27, 28)
(11) time average neutralization by electron oscillations and
tunable migmacell (Ref. 29)
(12) ion and electron morphodynamics (Ref. 30, 31), "tailoring"
of particle distributions in phase space (Ref. 23)
(13) fast fusion (See Sect. 2.1)
(14) high energy fusion (Sect. 3.1)
(15) advanced fuel fusion (Ref. 15, 19), or "clean fusion"
(16) dynamic non-linear stabilization (Sect. 2.7)
(17) bunched fusion (Sect. 6 of Ref. 23)
(18) diamagnetic increase of the mirror ratio (Ref. 32 and App.
A5)
2. ~ The "Philosophy" of the Migmacell System Design
The "philosophy" of the migmacell design differs from that of the governmental fusion power reactor programs with regard to (1) size and power density, (2) power gain, (3) power output per unit, (4) method of initiating and maintaining the fusion process, (5) time structure of operation, (6) extraction of fusion products, and (7) instabilities.
2.1 ~ Size and Power Density
For the ignited reactors it is believed that the larger the device is, the more likely it is to work. In contrast, our premise is that the smaller the fusion device is, the more likely it will work.
Migmacell is about 1 meter in diameter. The fusion reaction volume is 0.01 to 0.1 m3, depending on the strength of the magnetic field on the superconductor that can be achieved. (Fig.1 [Not available])
The stabilizing effect of Larmor radii large relative to the size of the device is theoretically and experimentally known (See Sect. 2.7).
The smaller the device, the nearer the fuel to the superconductor, the more advantage it will derive from the magnetic field; the fusion power densities in any device is proportional to the fourth power of the field strength. The kinetic-to-magnetic energy density ratio, beta, in migma is expected to be near 1.
Diamagnetism has a small effect on the size of the Migma (Ref. 32). Because the migma density is peaked at the center (r = z = 0), the diamagnetic field carves out a "hole" in the B(r) at r = 0, while at the periphery, r = rmax, B retains nearly its original value. The ions are confined by the peripheral field even when the field at the center is zero. With the state-of-the-art superconductive magnet technology, we expect a fusion power density of 0.1 kw/cm3 (this is 2 or 3 orders of magnitude higher than that expected for "mainline" fusion devices, Ref. 33). The fuel ions will be compressed to a smaller volume accessible to external manipulation: instabilities may be controlled by a number of corrective actions used in electronic circuits and tubes (See Sect. 2.7).
High power density implies that a large fraction of the fuel content of the cell is "burned" per unit time. This we refer to as fast fusion. Our power balance calculations indicate the burn fraction in the range of 0.1 to 0.7 (Table 2). This is an order of magnitude higher than expected for the mainline devices.
Experiments with such small devices are relatively easy to commit. The hardware of an experimental unit costs less than $1 million. Theories can be tested fast and rejected fast; designs and directions can be easily changed.
2.2 ~ Power Gain
The power gain of the "ignited" reactors, which is the aim of the mainline program, is infinity. In contrast, our stability considerations (See Sect. 2.7 and App. C) and the engineering requirements to implement them have convinced us that the lower the fusion power gain aimed at (the higher the ion energy), the more likely it is that the fusion power device can be made operational and useful. This ism of course, true only as long as the system is self-propelled, i.e., Q > 1. Our detailed calculations (See Sect. 4) based on the state-of-the-art technology give the gain:
(1) Q = power input / power output = 1.5 to 3.5
The advantages of the low gain are consequences of the physical and engineering advantages of high-energy (MeV) fusion, as opposed to thermonuclear (KeV) fusion (See also Sect. 3.1 and Fig. A1 and A2 in App. A).
The adverse effect of the low gain is the high "circulating power" needed. A large fraction of the fusion power generated must be fed back into the system. This results in: (1) an increased fuel consumption, and (2) the requirement that the conversion of the fusion energy into electricity be done with the efficiency higher than that of thermal conversion.
These difficulties may be offset by the facts that: (1) the cost of fusion fuel, such as deuterium or boron may be negligible compared to the capital cost; (2) the use of advanced fuels, whose fusion products are charged particles, makes high efficiencies les difficult because the direct conversion into electricity becomes feasible. As shown in Sect. 4 and 5, the efficiencies in the 80-90% range that are desirable, appear to be possible in direct conversion. Yet, these high efficiencies are not essential. If the "burn" percentage can be increased, efficiencies as low as 30% will make the migmacell operational, although only marginally so (See Table 2).
2.3 ~ Power Output Per Unit
While the typical design figure for the ignited reactors is 5000 MW, we are aiming at a power output per migmacell in the range of 100 KW to 5 MW. A large power station can be built by multitudes of power cells. Advantages of having the power stations consisting of 10s to 1000s of identical low to medium power units are:
(1) Economy of mass production. This would introduce standardization in the power plant construction, a feature long desired by the utility industry.
(2) Power stations can be made large or small. As a result, the pattern of the power distribution in the nation will change. Local stations (e.g. for peak load) would become possible. The costly power transmission can be reduced. A study of the effects of a migmacell-based power production on distribution of electric power has been carried out by Power Technologies, Inc. (Ref. 34).
(3) Planning and construction time would be reduced, thus reducing the already high and increasing indirect costs of inflation and interest during construction.
(4) Power plant size can be increased with load eliminating the need for large overcapacity to allow for future growth.
2.4 ~ Method of Initiating and Maintaining the Fusion Process
Ordered motions of the fuel ions are the key to the operation of migmacell. Random motions of fuel ions have been the main obstacle to achieving the controlled fusion conditions in plasma. Random motions can be easily confined by gravitational and inertial methods (stars and the fusion bomb), but not necessarily by the magnetic confinement. The nature of the magnetic forces acting on the randomly moving particles of both signs of charge is intrinsically different from the gravitational and inertial forces. The latter are independent of the sign of charge and the direction of motion; the former are not.
Migmacell is based on ordered motion of ions, thus the magnetic field acts like a guiding field rather than the "pressure" field. Of course, the ion motions in a migmacell are ordered only to a certain degree and in comparison with a magnetic bottle filled with small Larmor radius ions. The orbits pass through the center, thus have "zero" or small canonical angular momentum. At higher densities the orbits will spread; however, the system will conserve some of its salient properties such as the peaked central density and the ion Larmor radius comparable to the size of the plasma.
Migma is not electrically neutral. Like all mirrors, the ambipolar potential of migma is always positive. Because of its small size, the positive potential is expected to be maintained to a good degree of precision by a fast-response electronic feedback control of the number of electrons in the migma. In such a system in which both the electric and magnetic fields are present, the electron motions become quasi-ordered too. The electrons in migmacell are expected to exhibit motions similar to those of the "solid body rotation" of the electron space charge in a magnetron (Ref. 27, 28), as well as oscillations (Ref. 29, 30, as in a Barkhausen oscillator in a triode tube).
This "synthetic" mixture of the migma ion and electrons we refer to as "electron impregnated migma" or "eligma". We note that, if the surplus of the positive over negative charge in eligma does not exceed the "space charge limit" as defined in accelerator physics, migma orbits may be expected to behave nearly like the single particle orbits even at high densities.
2.5 ~ Time Structure of Operation
The mode of injections into migmacell is either DC, or a continuous train of "buckets", or "bunches", as in linacs. This is in contrast to the colossal bursts every few seconds of the plasma machines. We reject the idea that one should build a fusion engine the same way one builds a fusion bomb. The engineering considerations give practical preferences to steady operational-energy generators. The utilities have no experience with electric generators operating in big pulses.
2.6 ~ Extraction of Fusion Products
The small size of migma renders it possible to extract the charged fusion products at the energies near to their original energy as released from the reaction, that is in the MeV range. This contrasts with other approaches in which it is assumed that the fusion products would thermalize before extraction. It also facilitates removal of high charge nuclei which "poison" fusion reactors.
By having the nuclei produced in fusion in the energy range of 1 to 10 MeV, one can apply magnetic beam-shaping methods such as magnetic cusps, to transform the curly radial migma motions of those nuclei into a beam. This process is the reverse of the "electron ring acceleration" in which a beam is transformed into a curly, radial movement by a magnetic cusp (Ref. 35).
Once the nuclei produced in fusion are made into a beam, their kinetic energy can be converted into electric energy by directing this beam into a decelerator, i.e., an accelerator at a repulsive potential. As the beam is being slowed down, it will give its kinetic energy to the rings of the decelerator via the vacuum displacement current. This, in turn, will result in megavolt potentials suitable for power transmission. The exiting beam can be modulated [ ...line of text cut off at bottom of page... ]
2.7 ~ Instabilities
For the reasons listed at the end of this section, we expect the migma to be more stable than other plasma devices. The word "stable" has a relative meaning. Every engineering system involving energy exchange would exhibit various intrinsic instabilities if the external or internal corrective mechanisms were not used. Thus, we consider it prudent to keep a watch out for the appearance of collective oscillations and to have a developed repertoire of general techniques for treating any which could present a problem. Our effort is to make the diagnostics sufficiently sensitive (Ref. 25, 26) to detect the appearance of collective oscillations well before they reach the levels that produce significant losses. The effort is directed to making the power cell small and accessible to both passive and active corrective measures to de-energize the instability growth. This is in contrast to the mainline programs aimed at building bigger and bigger devices in the belief that there is a certain size at which the system will overcome the effects of instability.
Several methods of dealing with hypothetical instabilities have been borrowed from electronic engineering. One such method is "dithering", a non-feedback technique known in engineering and described by Lashinsky (Ref. 36). The salient feature of dithering is that is possible to stabilize some instabilities by the continuous application of a high frequency signal without the need to sense and feed back the incipient instability. It is our plan to apply dithering to the migmacell by modulating the beam injection. That is, the stored ions will be the main agent of fathering we foresee, playing the role of the grid in an electronic tube oscillator. An interesting example of dynamic stabilization by modulation of an ion beam had been described by Decker and Levine (Ref. 36).
Other dynamic stabilization methods have been described in the same book (Ref. 36), as well as in Refs. 37, 38. Interaction of high frequency fields with the plasma has also been studied as a way of avoiding the most dangerous instabilities in a recent review (Ref. 39)
We are particularly interested in applying those dynamic stabilization techniques that are based on periodic and nonlinear corrective action, internal or external, because migma is a highly nonlinear system (the ion density distribution being one example). From our point of view, the elementary definition of the static instability, depicted by a ball on top of a convex surface, does not imply instability. Such an "unstable" configuration can be made dynamically stable by engineering means, in the same manner mercury can be dynamically forced to "float" on oil by vibrations (Ref. 40). Similarly, the "unstable" physical system known as the inverted pendulum, is the underlying concept of stabilization of the particle beam in accelerators and storage rings, known as the strong focusing (Ref. 41). Stability of the strong focusing machines is so much better than that of the naturally stable weak focusing accelerators, that the latter are no longer built.
From our analysis (Ref 42), we list below the favorable aspects that will contribute to the stability of migma:
(1) The stabilizing finite Larmor radius effect has been well-known since the Rosenbluth-Krall-Rostoker paper (Ref. 43), and was later shown to include the M = 1 flute mode (Ref. 44, 45)
(2) The configuration of centrally focused orbits will generate a central core with a fair degree of isotropy in the mid plane as a result of energy and angular momentum spread. This configuration of orbits suppress the negative mass instability. The mixing of ion trajectories in the core should provide local stability for electrostatic perturbations. The high energy ions will simulate a high ion temperature that should favor Landau damping effects, locally, in the core where trajectories are nearly rectilinear.
(3) The central density gradient is expected to reduce or suppress beam-driven instabilities. It was shown by Bers and David (Ref. 46) that the presence of a density gradient in the beam direction, reduces the instability growth rate, and also reduces the amplitude level of the electric field generated by the instability in the nonlinear regime as compared with the gradient-free case. Thus we expect to be able to reach a self-exponentiation regime in which the beam is trapped mainly by the migma core.
(4) A relatively high electron temperature is expected (around 100 KeV) as the density increases. This will provide a stabilizing effect because of the enhanced Landau damping of electron waves along the magnetic field, combined with the short axial length of migma.
(5) We add the following points of merit for migmacell. Assuming the validity of typical analysis of the plasma dispersion relation for migma, it can be shown:
(a) that the frequency convective loss-cone is stable for Lm / RL < 65 (where Im is the length between the mirrors and RL is the ion Larmor radius).
(b) that the negative energy mode, which would dominate at low density (w2pi/w2ci < 1) is stable for Lm/RL < (mi/me) ½.
(c) that the Alfven ion cyclotron mode, which is driven by p | > p|| and is characterized by an axial wavelength comparable to the mirror length, is stable for Rp/RL ~ 4 where Rp is the plasma radius (Baldwin, Ref. 47)
There is a fourth instability connected with the loss-cone, the drift-cyclotron mode. It is a possible "candidate" to appear in migma experiments at higher densities. This is a non-disruptive type of instability, which is very sensitive to the presence of small amounts of warm plasma, as was shown in the LLL experiments (Ref. 48)
In summary, out of the four loss-cone-like instabilities, three are inherently stable due to the geometry of the migma device, and the rather high electron temperature that results as a consequence of the ~ MeV ion injection. However, the assumption that the ordinary stability results can be applied to migma must be examined carefully. Appendix C is devoted to this point and to our overall evaluation of the stability problem.
3. ~ Remarks on Scientific Background of the Migmacell Concept
So different is the "philosophy" of the Migma Program from the official thinking that the initial reaction of those who have been exposed to the plasma fusion reactor concepts for many years is one of disbelief in its scientific "legitimacy". Some ideas and concepts will be discussed below. Reader is also referred to Appendices A, B, and C.
3.1 High Energy Fusion
The salient feature of the migma concept is that, because of the ordered ions motions, storage and collision of high-energy ions, at the levels of MeV, becomes possible. This should be compared with thermonuclear temperatures in plasmas, which are at KeV levels. Already in Migmacell models 2 and 3, deuterium and helium-3 ions have been stored in the migma-like self-colliding orbit distribution, with an average collisional energy of 1 MeV. To achieve the same collisional energies in a plasma, the plasma would have to be heated to a temperature in excess of 10 billion degrees Kelvin (The average "temperature"-energy relation is To(K) ~ 107 E(KeV).
The mere fact that the confinement of high-energy ions is feasible opens up a host of advantages. They can be divided into three categories: (i) advantages in the single-particle or "classical" properties; (ii) advantages in the collective behavior, and (iii) practical advantages.
(i) Single-Particle or Classical Properties ~ Referring to Figure A1 (in App. A), the reader can see that at the MeV temperatures, the fusion reactivities, <ov>, leading to energy gains are greater than the reactivities for all the electromagnetic processes which lead to the energy losses, this, coupled to the focusing action (Ref 49) results in low classical end losses (Ref 31) compared to plasma mirrors. This is described in Appendix A and B.
(ii) Collective Behavior ~ Both the large Lamor radii of the migma orbits and the rosette-like configuration (zero canonical angular momentum have been known to have stabilizing effects against collective phenomena); see Sect. 2.7 and App. C.
(iii) Practical Advantages ~ The practical advantages are that high energies (Ref. 51-55) render it possible to use the ultimate advanced fuels such as non-radioactive deuterium, He3 and boron, which cannot be easily confined in a random, thermonuclear system with the magnetic fields available. The experiments can be carried out now using real fusion fuel, while in most plasma fusion experiments of today, the light hydrogen (which does not undergo fusion) is being used to simulate the process, because of the inherent difficulties in handling the real fuel, tritium, and its contamination.
Experiments can be done now at the "temperatures" equivalent to those of the reactor conditions, thus avoiding waste of time in solving the problems at the low (KeV) temperatures which are irrelevant to the operation of an advanced fuel power source.
3.2 ~ Theoretical and Experimental Base
The migma experiments and theory are based on the established standards of scientific rigor and technological reality. No fictional technology is involved, Concepts and ideas are backed either by experiment or calculations (Ref. 19, 31, 49, 50). We have generalized the Lawson criteria to make it applicable to non-ideal physical systems (Ref. 51-55) which rendered it possible to analyze the detailed behavior of the engineering of the fusion power systems. Critiques (Ref. 52, 58) of this revision have been found to be based on differences in philosophies (Ref. 52, 58; see Sect. 2). Experimental results are obtained with both the statistical and systematic errors equal to or smaller than those in typical plasma experiments (Ref. 24, 59, 60).
Another example is the self-consistent calculation of the effects of diamagnetism on energy balance (Ref. 32). Its conclusion is that a migma power cell, to yield about 0.5 MW of fusion power, is conceivable within the realm of the state-of-the-art magnet technology (Bo = 5.3 Tesla). This is in rough agreement with an earlier calculation (Ref. 62) which, however, does not include a factor for the effects of focusing in the Z direction. Noting (from Equation 12 of Ref. 32) that the fusion rate scales as Bo4 R4 when <Beta> ~ 1, it seems that advances in the technology of superconductive magnets may permit significantly higher fusion power per cell.
These results (Ref. 32) are diametrically opposite to the official unpublished results of Robson, et al. (Ref 63). From their non-self-consistent calculations (based on a non-physical model of migma), these authors concluded that the diamagnetism limits the fusion power to such low intensities (a small fraction of a watt), that the synchrotron radiation power will always exceed the fusion power. In their "Final Report" (Ref. 63), the authors presented this incorrect conclusion as the "fundamental obstacle" which will prevent Migma from working as a power source. This is an example of the use of official secrecy to hide mistakes from the scientific community.
Our energy balance computations typically include all energy-gain and loss processes, involving up to 100 parameters to describe non-ideal reactor conditions (Ref. 64-67). Monte Carlo codes are used to simulate the operating conditions of a fusion reaction volume (Ref. 68). These data are accepted only when they agree with the approximate analytical methods.
Our technological planning is done by management consultants (Ref. 16), as are the economic projections (Ref.69).
3.3 ~ Irrelevance of the Instabilities Observed in DCX-1
The instabilities observed in an early (1950s) mirror machine known as DCX-1 which had similar shape of the magnetic field to migma, are not relevant to migma. The DCX-1 was never operated in the pure migma-like mode. The rosette-like migma orbits pass through the center of symmetry of the magnetic field and have "zero" canonical angular momentum. In contrast, nearly all DCX data were obtained in the "circular orbit" mode, in which the ions circulated in an orbit whose center is the center of the magnetic field. Moreover, it is not a self-colliding orbit, thus it is not relevant to high-energy fusion; it can be used only to heat the plasma.
However, there were two short DCX runs in which both the circular and migma-like orbits were simultaneously established. Although the ions were aimed at the center, pure migma orbits could not be made. This was because the beam was so wide ( ~ 5 cm / whm) that a significant number of ions always spilled out of the rosette orbit and entered the circular orbit as well. Even under these unclean conditions, the remarkable stability of migma orbits (Ref. 70) was observed:
When run in the pure circular mode (non-migma mode), the DCX-1 negative-mass instability threshold was observed at anion density of 10 5 ions cm3.
When run in the mixture of circular plus migma mode, the system became 100-fold more stable. The instability threshold increased by at least 2 orders of magnitude to >107 ion cm3. The experimentalists proved, by "scraping" the circular orbits, that the remnant instability originated entirely from the ions in the circular orbits (Ref. 70); the instability disappeared when circular orbit was destroyed.
In the Migmacell III experiments, we have exceeded this density by another order of magnitude (above the DCX-1 threshold in the migma-plus-circular mode), without observing any instabilities (Ref. 24). By focusing the injected beam to an order of magnitude smaller spot (<0.3 cm / whm), no ions were allowed to enter the unstable circular orbit and the negative mass instability was avoided.
The DCX and Migma III results are in agreement with the predictions (Ref. 71), obtained by Monte Carlo simulations, of negative-mass instabilities for ions in the migma-type orbits.
Why did the DCX-1 experimentalists not pursue the migma configuration in the 1950s? The reader is reminded that the principle of self-colliding orbits was published only in 1970. The physicists were unaware of the unusual stability properties of these large gyro-radius orbits with "zero" canonical angular momentum. Furthermore, the applicability of the principle of self-colliding orbits to particles of the like charge was pointed out in late 1971 (Ref. 21), and in more detail only in 1973 (Ref. 22). Prior to that, the idea of igniting fusion by direct collisions rather than by heating was practically nonexistent in the literature. High-energy ions were being injected into the DCX machines as a means of collisional heating of the plasma. The purpose of the program was to degrade the injected ions to thermonuclear (KeV) temperatures, rather than to maintain their energy in the near MeV range.
Therefore, I must conclude the DCX experimentalists did not pursue the migma orbits --- in spite of their proven stability --- for the lack of theoretical motivaion to make fusion in direct collisions.
Theory of the stability of the migma-type orbits does not exist. The densities at which a migmacell will produce an excess energy (1014 ions/cm3) have already been achieved in plasma physics. In addition to the arguments in favor of the migma stability listed in Sect. 2.7 and Appendix C, the migma orbits should be more stable against perturbations because of their 100 to 1000 times higher energy. A local electric field of 105 V is a 1000% perturbation to thermonuclear orbits, but only a 10% perturbation to migma.
Plasma orbits are unstable because they have properties of a fluid (adiabatic orbits). The large gyro-radius migma orbits have properties of an elastic spring (non-adiabatic orbits) of high rigidity.
Some of the proposed techniques involved in the migmacell operation are yet untested, and therefore there is a danger of the unknown. No known calculable physical effect or phenomenon has been shown to present an obstacle to the operation of migmacell. The migma concept has not been proven and has not been disproven. Only the experiments will decide on the migma stability at increased densities.
4. ~ Fusion Power Generated in Migmacell
Viability of migma as power amplifier depends on the power balance. Our economic projections (Ref. 69) have shown that, in order for a migmacell to be viable, it must have fusion power in excess of 100 KW. A self-consistent calculation (Ref. 32) shows that migmacell can operate in the regime in which the ratio of the kinetic and magnetic energy density is unity, Beta = 1.
We present here the results of calculations (Ref. 68) of the power balance which shows that tens of Megawatts per m3 of fusion power density can be produced in migmacell. This program requires much computer time and is expensive. It has been used to develop analytical models which can show trends in important parameters. Only the first stage of the calculations has been completed, which assumes the mirror ratio produced by the external magnetic field only (case A, "semi-open" mirror). For the mirror ratio enhanced by the diamagnetic effect, this author presents his estimates (case Bm "semi-closed" mirror). No numbers are given for "plugged mirrors". Therefore, the presented power balance results are conservative.
4.1 ~ Three Fuel Cycles
Three fuel cycles have been considered: (1) pure He3, (2) pure D, and (3) mixed D + He3.
For each of the fuels, the results for two cases, A = "semi-open" mirror, B = "semi-closed" (diamagnetic mirror ratio) in Tables 1, 2, and 3.
4.2 ~ Results for Case A: "Semi-Open" Mirror
Pure He3 (1A) and pure D Fuels (2A): Results show a fusion power density of 10 Megawatts/m3 for pure D fuel, for a 7 tesla external field, and the scaling proportional to the fourth power of the field strength. This is shown in Figure 2.
Figure 2 ~ Fusion Power in MW
Mixed D-He3 Fuel (3A): Using the results for the pure fuels, we estimate a fusion power density of 30 Megawatts /m3 for D-He3 fuel. These fusion power densities, 2 to 30 Megawatts/m3, are achievable at the average ion densities in the range 5 x 1013 - 1014 ions/cm3 which have already been reached in the major plasma devices.
4.3 ~ Results for Case B: "Semi-Closed" Mirror
Diamagnetism increases the effective mirror ratio which, in turn, increases the burn.
Pure He3 (1B) and Pure D (2B): Results show a fusion power density of 6 Megawatts/m3 for pure He3 and 60 Megawatts/m3 for pure D.
Mixed He3-D (3B): Using the results for pure fuels, we estimate a fusion power density of 100 Megawatts/m3 for the mixed He3-D fuel
4.4 ~ Power Flow Diagram
The results have been displayed in terms of the Power Flow Diagram shown in Figure 3. The accelerator (ACCEL) injects an ion current I (amp) at the accelerating voltage V (MV), that is, the beam power PI (MW) into the Migmacell. The accelerator efficiency is nI = PI / Pcirc, where Pcirc = the circulating power. The beam trapping efficiency to make migma is not a free parameter, but is compiled as a function of migma density and other factors. The fusion power released is determined by the computed quantity: BURN percentage = (equiv. Fusion rate): ion loss rate due to multiple coulomb and nuclear elastic scattering.
The fusion rate plus power output from the cell is partitioned between charged particles, CP; neutrons, n; electromagnetic radiation, r; and leaking electrons, e. Charged particles are split into two components: charged fusion products and non-fused fuel ions. The power carried out of the cell by the sum of these two components is labeled PCP, and that taken away by the neutrons, Pn. The power carried by radiation comes only from the stored fuel ions, because the fusion products storage time in migmacell is short. The sum of the radiation and electron carried power is labeled Pr,e.
The efficiencies for direct and thermal conversion are nDC and nTC respectively, so that nDC = PDC / PCP and nTC / (Pn + Pr,e). The waste heat HEATDC = PCP (and similarly for TC). The net electric power output is:
Pnet = PDC + PTC - Pcirc.
The waste heat from ACCEL is:
HEATacc = Pcirc - PI.
Figure 3 ~ Power FLow Diagram
4.5 ~ Discussion of Efficiencies
The efficiencies are displayed in Table 1
Accelerator Efficiency, nI : So far, there has been no demand to the accelerator manufacturers to increase the efficiencies of ion accelerators. Efficiencies of commercially produced 2 MeV electron accelerators with the isolated curve transformer, ICT, are: power line-to-tube = 0.9; and tube-to-beam = 0.9. In a mature design, some or all Pcirc from direct converter (decelerator) to the accelerator will flow directly, from each ring of decelerator to the corresponding accelerator ring, i.e., deceleration and acceleration will be in the same tank. Thus, we take: nI = 0.9. We think the eventual injector will be Linac whose n is known to increase with the beam power and can probably exceed 0.9 under a development program. An inverse cyclotron-type a.f. direct converter has been proposed, too. The natural operating frequency of this converter can be made equal to the optimum accelerating frequency of the Linac.
Thermal conversion efficiency: nTH = 0.4 was used in all cases.
Direct conversion efficiency, nDC : Studies of direct conversion collectors in the KeV range at LLL have indicated nDC = 0.88 - 0.97. The migma program envisages an efficient system using the decelerator technique.
Minimal efficiency for direct conversion nmin is obtained by seeking the value of nDC when Pnet = 0 which implies "engineering breakeven". Nmin are given in Column 3 of Table 1. We see that the migma system will be self-sustained for nDC as low as 0.3 for mixed fuels. The situation is most difficult for pure He3, which requires nmin = 0.7 with the state-of-the-art technology. We note, however, that in arriving at nmin, we assume the simplest conversion into heat, nTH = 0.4, without the advanced thermal conversion methods such as electrochemical with nTH > 0.65.
A simplified relation between the minimum efficiency, nmin, and the ratio of the fusion raction energy to the energy invested in the colliding ions, W/2Ti is given by:
(2) 
Equation (2) is obtained from Equation (9) of p. 79 of Ref. 19, with ni = nf = nnf = nmin and G = 1 (breakeven). It shows a weak dependence of the efficiencies on G or the more commonly used Q. Letting nt <ov> = 0.5, we obtain the minimum efficiencies for the three types of fuels:
(3) Pure He3: nmin ~ 0.74
(4) Pure D: nmin ~ 0.66
(5) Mixed He3: nmin ~ 0.34
The values (3-5) should be compared with more accurate estimates in Table 1.
4.6 ~ Technical Problem I: Superconductive Magnet
The superconductive magnet that can be designed and made today would not allow for space between the migma chamber and the magnet structure, which must be occupied by the neutron modulator and absorber. Pure D fuel will be releasing 1.1 MW, and He3-D, <0.1 MW of neutron power. This power cannot be taken by the superconducting magnet cooling system, as it will result in a very high rate of liquid helium boil-off. Only pure He3 is neutron-free. Therefore, we are forced to consider only the He3 fuel as the possibility for our first migma fusion power amplifier.
4.7 ~ Technical Problem II: Ion Current
Column 1 of Table 2 reveals the problem # II: Ion currents of the order of 1 to 2.4 amps are needed at Megavolt accelerating voltages. Technology of ampere ion accelerators at Megavolts is under development for the super high energy accelerator at CERN in Geneva. Also, R.Martin is developing an 0.5 amp 4 MV machine for inertial fusion at Argonne. From an accelerator that may be built commercially, we hope to get 0.03 amps of He3. This limits the power output to about 1% of the values listed in Columns 6-8, i.e., from 6 MW to 60 KW (case A), and from 180 KW to 2 KW (case B)
5. ~ Conclusions
Referring to Tables 1, 2, and 3, a number of conclusions can be drawn. We selected some of them:
Conclusion I ~ Using mixed fuel D-He3, driven power amplifiers with gain Q = 3 would produce net useful power of 2 MW, if direct conversion efficiency of 0.9 can be achieved. However, the superconductive magnet, giving 7 tesla in the middle of the cell, of sufficiently large size needed to avoid the neutron-induced liquid helium boil-off is not within the state-of-the-art.
Conclusion II ~ Mixed fuel D-He3 migmacell would operate at the engineering breakeven, with as low a direct conversion efficiency as 0.3, if the neutron problem can be handled.
Conclusion III ~ Pure D fueled migmacell could generate 0.6 MW with direct conversion efficiency of as low as 0.7, when 2 amps of D3+ ions current at 2 MeV becomes available, and if the neutron problem can be handled.
Conclusion IV ~ Pure He3 fuel is the only one for which a large enough superconductive magnet can be built with certainty, but it requires an accelerator delivering 1 amp of He3+ ions at 4 MV, in which case it will have a fusion gain of 2 and a useful power output of >1 MW, provided a direct conversion efficiency of 0.9 is possible.
6. ~ Our Experimental Progress
We have built four operational laboratory models of migmacell named Migma I, II, III and IV. We did experiments with the first three models. We have achieved:
6.1 ~ a reliable production of D (and He3) migma (Fig. 4, 5, 6);
6.2 ~ an energy confinement time of (2.21 + 0.05) seconds (Fig. 7. 8);
6.3 ~ a collisional energy of about 1 MeV. To achieve the same collisional speeds in a plasma, plasma would have to be heated to 10 billion degrees centigrade, this is 102 to 103 higher than the equivalent temperature of plasma fusion devices (Fig. 9);
6.4 ~ the total number of deuterium ions stored in Migma III of 1.4 x 1010. This number is limited by the injection rate and vacuum, which were 0.1 and 6 x 10-8 torr, respectively. The volume average ion density was nv = ( 1.25 + 0.4 ) x 108 cm-3; the central peak density nc = ( 2.2 + 0.7 ) x 109 cm-3; and the effective average density neff = 3.5 x 108 cm-3.
Migma has exhibited no instabilities at this density. In contrast, a plasma machine with the similar embodiment, DCX-1 of the 1950s, had shown clear "negative mass" instability at 1000 times lower density. Our theoretical calculations show that the migma orbit configuration ("rosette") is responsible for this stability (See Sect. 2.7).
6.6 ~ The product of density and confinement time achieved is:
(6) nvt = 4 x 108 scm-3 and
(7) nct = 5 x 109 scm-3
This is a 104 fold improvement over Migma III.
6.7 ~ The overall performance indicator (Ref. 75, 76), the product of temperature, density, and time reached Tnt is 1 to 5 x 109 MeV sec cm-3.
Figure 10 shows that this value Tnt has put migma in the same ball park as the leading fusion devices. We wish to point out that while the new criterion (Ref. 75, 76) is better than that of Lawson, it does not provide information as to how near the device is from making energy. The unified criterion (Ref. 77) of proximity to controlled fusion is an attempt to provide that.
6.8 ~ Migma IV is expected to leap 100 fold to 1000 fold in the overall performance from Migma III. This is expected by the 100-1000 fold increase in density and 3 fold increase in the confinement itme. To accomplish this, a 100 times better vacuum, and 20 times better ion injection is needed. In the test runs in December 1976, we have achieved (ref. 74) the pumping speed of 10,000 liters/sec., and a vacuum of better than 10-9 torr has been maintained while 0.5 ms of ion beam (7 fold increase over Migma III) was being continuously injected into the chamber. The experiments with this system could not be done because of lack of funds. The tests with Migma IV are considered "critical" because the migma fuel will enter the regime in which the ( wp / wc )2 exceeds 10.
7. ~ Economic Projections of Migma Fusion
An elaborate economic study, using the generally established procedures in estimating and projecting capital, operating and R & D costs for power plants shows that migma fusion can generate electricity for 1cent/KW to 6 cent/KWh, depending on the level of development which is competitive with present power sources. It also indicates that present power sources are subject to large increases in costs.
These projections have been made without invoking a crash program, i.e., on the conservative assumption if no extraordinary intense development effort that may be dictated, for example, by a crisis.
8. ~ Acknowledgments
The concept of fusion "energy amplifier" was first discussed by Ribe (Ref. 78).
Thanks are due to Robert A. Miller for his invaluable aid in preparation of this paper; to Fausto Gratton and Stephen Menasian for their remarks.
Thanks are due to David Bird, Nadine Henley, H. Snowden Marshall and other friends an colleagues for their encouragement to Maglich Energy Group, which operates Fusion Energy Corporation, and their financial support during the crisis.
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