Confinement performance predictions for a high field axisymmetric tandem mirror

From the earliest days of fusion research, Richard F. Post and other advocates of magnetic mirror confinement recognized that mirrors favor high ion temperatures where nuclear reaction rates begin to peak for all fusion fuels. In this paper we review why high ion temperatures are favored, using Post’s axisymmetric Kinetically Stabilized Tandem Mirror as the example; and we offer a new idea that appears to greatly improve reactor prospects at high ion temperatures. The idea is, first, to take advantage of recent advances in superconducting magnet technology to minimize the size and cost of End Plugs; and secondly, to utilize parallel advances in gyrotrons that would enable intense electron cyclotron heating (ECH) in these high field End Plugs. The yin-yang magnets and thermal barriers that complicated earlier tandem mirror designs are not required. We find that, concerning end losses, intense ECH in symmetric End Plugs could increase the fusion power gain Q, for both DT and Catalyzed DD fuel cycles, to levels competitive with steady-state tokamaks burning DT fuel. Radial losses remain an issue that will ultimately determine reactor viability.

Some of the important residual instabilities of Tokamak and Tandem Mirror fusion devices are trapped particle modes. We discuss control schemes for these instabilities using a Langmuir probe sensor and a Langmuir probe or a pair of electrostatic plates as a suppressor in the low temperature plasma of Linear Machines. We describe a remote suppressor of modulated neutral beam which appears to be highly promising in the context of high temperature fusion plasma of Tokamak and Tandem Mirror reactors.

The advantages and feasibility of neutral beams with Z ≥ 3 formed from negative ions, accelerated to 0.5–1.0 MeV·amu−1, and neutralized, are investigated for use in tandem mirror reactor end plugs. A reactor plasma physics design incorporating these beams has been done with the result that such a reactor could produce Q's (ratio of fusion power to injected power) of 20–30. These beams thus might be a replacement for the currently proposed 200–500-keV neutral proton beams presently planned for tandem mirror reactors. Thus these Z ≥ 3 neutral beams could increase the potential attractiveness of tandem mirror reactors by offering a possible substitute for difficult high-energy neutral-hydrogen end plug beams.

This paper is largely devoted to tandem mirror and field-reversed mirror experiments at the Lawrence Livermore Laboratory (LLL), and briefly summarizes results of experiments in which field-reversal has been achieved. In the tandem experiment, high-energy, high-density plasmas (nearly identical to 2XIIB plasmas) are located at each end of a solenoid where plasma ions are electrostatically confined by the high positive poentials arising in the end plug plasma. End plug ions are magnetically confined, and electrons are electrostatically confined by the overall positive potential of the system. The field-reversed mirror reactor consists of several small field-reversed mirror plasmas linked together for economic reasons. In the LLL Beta II experiment, generation of a field-reversed plasma ring will be investigated using a high-energy plasma gun with a transverse radial magnetic field. This plasma will be further heated and sustained by injection of intense, high-energy neutral beams.

The path to practical fusion power through plasma confinement in magnetic fields, if it is solely based on the present front-runner, the tokamak, is clearly long, expensive, and arduous. The root causes for this situation lie in the effects of endemic plasma turbulence and in the complexity the tokamak's ''closed'' field geometry. The studies carried out in the investigations described in the attached reports are aimed at finding an approach that does not suffer from these problems. This goal is to be achieved by employing an axisymmetric ''open'' magnetic field geometry, i.e. one generated by a linear array of circular magnet coils, and employing the magnetic mirror effect in accomplishing the plugging of end leakage. More specifically, the studies were aimed at utilizing the tandem-mirror concept in an axisymmetric configuration to achieve performance superior to the tokamak, and in a far simpler system, one for which the cost and development time could be much lower than that for the tokamak, as exemplified by ITER and its follow-ons. An important stimulus for investigating axisymmetric versions of the tandem mirror is the fact that, beginning from early days in fusion research there have been examples of axisymmetric mirror experiments where the plasma exhibited crossfield transport far below the turbulence-enhanced rates characteristic of tokamaks, in specific cases approaching the ''classical'' rate. From the standpoint of theory, axisymmetric mirror-based systems have special characteristics that help explain the low levels of turbulence that have been observed. Among these are the facts that there are no parallel currents in the equilibrium state, and that the drift surfaces of all of the trapped particles are closed surfaces, as shown early on by Teller and Northrop. In addition, in such systems it is possible to arrange that the radial boundary of the confined plasma terminates without contact with the chamber wall. This possibility reduces the probability of so-called ''temperature-gradient'' instabilities, known to be endemic to closed systems. Finally, the open-ended nature of the field readily allows the control of the radial potential distribution, a circumstance that has been shown, for example in the Gamma 10 tandem-mirror experiment at Tsukuba Japan, to suppress drift-type instability modes. Standing against all of these attractive properties of axisymmetric mirror-based systems is the fact, shown early on, that such systems are prone to MHD ''interchange'' instabilities, one in which the plasma column drifts transversely, at a rate far above classical transport. Observed early on, the ''cure'' that was universally adopted, as first demonstrated in the famous ''Ioffe experiment'', was to abandon axisymmetry and employ so-called ''magnetic-well'' fields, ones in which the field increases radially and axially from its interior, strongly suppressing the MHD interchange mode, up to plasma ''beta'' values approaching unity, observed in the 2X2B experiment. When the tandem mirror concept was introduced in 1976 every experiment that was constructed employed various combinations of non-axisymmetric coil configurations (''Baseball,'' and ''Yin-Yang'' coils) to create the magnetic fields. But it came at a heavy price: non-axisymmetric fields gave rise to new non-classical loss channels, and the complexity of the fields introduced difficult engineering problems. It was well recognized at the time that it would be highly advantageous to preserve axisymmetry of the tandem mirror coils, but there was no apparent way to stabilize the ubiquitous MHD interchange mode. A decade later a way to accomplish this end was analyzed theoretically, and, a few years later successfully demonstrated experimentally, in the Gas Dynamic Trap (GDT) experiment at Novosibirsk. The concept: the presence of a sufficient amount of plasma on the expanding field lines outside the end mirrors of a mirror machine can act as an ''anchor,'' MHD stabilizing the interior, confined, plasma. Moreover, Ryutov's theory showed that the pressure of this anchor plasma could be orders of magnitude smaller than that of the confined plasma, and still be able to stabilize it. In the GDT, which operates in a collision-dominated region (as opposed to the near-collisionless mode of a tandem mirror), the effluent plasma, though much lower in density than that of the confined plasma, is sufficient to stabilize the central plasma, up to plasma beta values of 40 percent. Furthermore, once MHD stabilized, the confined plasma in the GDT exhibited no signs of plasma turbulence or enhanced cross-field transport, even in the presence of a substantial population of high energy ions produced by neutral-beam injection.

A time-dependent version of the steady-state radial transport model in symmetric tandem mirrors in Ref. [1] has been coded up and first tests performed. Our code, named SYMTRAN, is an adaptation of the earlier SPHERE code for spheromaks, now modified for tandem mirror physics. Motivated by Post's new concept of kinetic stabilization of symmetric mirrors, it is an extension of the earlier TAMRAC rate-equation code omitting radial transport [2], which successfully accounted for experimental results in TMX. The SYMTRAN code differs from the earlier tandem mirror radial transport code TMT in that our code is focused on axisymmetric tandem mirrors and classical diffusion, whereas TMT emphasized non-ambipolar transport in TMX and MFTF-B due to yin-yang plugs and non-symmetric transitions between the plugs and axisymmetric center cell. Both codes exhibit interesting but different non-linear behavior.

Cold neutral gas density has important consequences for the energy and particle balances of the hot ion plasma in the end cells of tandem mirrors. Charge exchange loss from cold gas penetration into this plasma detracts from the pressure in the end cells needed for magnetohydrodynamic stability of the mirror. Unfortunately, cold gas can be a by-product of neutral beam injection and of fueling. This report describes measurements of neutral pressure in the rf heated tandem mirror Phaedrus. The emphasis is on the dynamics of gas flow into the end cells, the effects of cold gas on the plasma, and on wall reflux for different wall conditions. The effects of neutral beams and neutral beam generated wall reflux are also studied. A numerical gas flow code is used to model the effects of plasma pumping, charge exchange, and wall reflux on end cell plasma parameters. The titanium sticking coefficient for hydrogen gas was determined to be 0.08±0.08. Wall reflux coefficients in the end cell were determined to be 1.4±0.2 without titanium gettering and 0.75±0.25 with gettering.

We describe a new axisymmetric tandem mirror concept which incorporates advances in physics understanding, recent experimental results and developing technologies. The tandem mirror concept consists of two small high magnetic field axisymmetric mirrors at the ends a solenoidal central cell which axially confines a high beta fusion plasma. High energy neutral beam Injection and high frequency electron cyclotron heating power are applied to the end cells which operate at higher density and temperature to provide both magnetic mirror as well as electrostatic axial plasma confinement of the ignited central cell plasma. Designs fueled with DT and, cat-DD are considered indicating a wide design space warranting further analysis as well as experimental investigations.

Summary form only given, as follows. Hyper-thermal neutral beam sources are developing for the next generation semiconductor manufacturing device. The collimator in the device contacts the plasma to extract ion beam and exchange the incident ion beam to neutral beam resulted in Auger effect on the collimator surface layer. Hence, the neutral beam energy is proportional to the voltage difference between the plasma potential and bias voltage on the collimator. However, the biased collimator affects on the plasma parameters, especially the plasma potential In this presentation, the effects of the collimator biasing on the plasma parameters have been investigated by using various diagnostics tools, Langmuir probe, capacitive probe, emissive probe and grid ion energy analyzer. Ar and He plasma were used for the research. In addition, the effects of the collimator's physical size will be discussed on the plasma parameters.

Strong one-pass absorption of high-power microwaves is observed at the fundamental electron cyclotron resonance in an axisymmetric end mirror of the GAMMA 10 tandem mirror [Phys. Rev. Lett. 55, 939 (1985); Phys. Fluids 29, 2781 (1986)]. The radial profile of microwave power deposition is directly measured without the influence of wall reflection. It coincides with that of the axial flow of warm electrons driven by the fundamental heating as well as with that of the plasma potential at the resonance. This indicates that strong electron cyclotron heating largely affects the potential formation through driving an axial flow of warm electrons.

Because their energies greatly exceed the plug potential, fusion reaction alpha particles in a tandem mirror reactor will be mirror confined rather than electrostatically confined by the end plugs. Hence, the alpha particle distribution function will have a loss cone. This anisotropy in the distribution function is shown to destabilize Alfvén waves in the central section of a tandem mirror reactor. The wave equation with a modified cold plasma response is used to determine the radial mode structure and real frequency of the Alfvén waves in cylindrical geometry. The growth rate is calculated from the resonant particle part of the plasma response. Destabilization of the wave occurs due to a cyclotron resonance of the alpha particles. The resonant interaction of the wave with the alpha particles will pitch-angle scatter the alphas into the loss cone, effectively widening the loss cone. The instability will cause a substantial loss of alpha particle energy unless the central cell is characterized by small diameter, sharply peaked radial profile, low magnetic field, and large mirror ratio. A recent ‘‘axicell’’ reactor design is found to be stable.

A tandem-mirror plasma has been sustained and heated by rf alone without the need for neutral beams. End plug density and energy are maintained by ion cyclotron-resonance heating which traps and heats a fraction of the central-cell loss stream. The central-cell plasma is maintained by gas fueling and rf heating. Magnetohydrodynamic stability limits the ratio of the central-cell to plug plasma pressure, and the central-cell electron temperature must be kept high enough for ionization. A quasi steady state is achieved that lasts much longer than the decay times of the plugs and central cell.

An inner mirror throat of the plug/barrier cell is one of the noticeable locations in the tandem mirror GAMMA10, because the location is the most suitable for a measurement of the ions bounced by the plug potential, which are essential for the tandem mirror confinement. A lithium beam probe was designed as a main part of the diagnostic system to measure the radial profiles of the electron and neutral particle density at the inner mirror throat. A neutral lithium beam is injected into the plasma and the light emitted from the beam is detected. We estimated the upper limit of the plasma density measurable by the lithium beam probe and discussed validity of the reconstruction for various types of radial profiles. We adopted, at first, a Gaussian type of radial profile of the density with the radius of 2.5 cm for the estimation of the upper limit of the density. It was found that the profile reconstruction was carried out well up to the peak density of 5 × 1013 cm-3, and also well even in the non-axisymmetric radial profile. This method is quite appropriate for the measurement of the density profile at the inner mirror throat.

In order to improve the axial confinement, in the tandem mirror machine, the electrostatic potentials are created on both sides of the machine. Usually, thermal barrier potential is created at the midplane of the plug/barrier cell. We note that the electrostatic potential at the Inner Mirror Throats (IMT) is able to play an important role acting as a barrier of the electron flow from the central cell to the plug cell. We examined the influence of the IMT potential on the electron flow by calculation, and it was found that the IMT potential acted effectively as the thermal barrier. In consideration of the undesirable condition at the IMT region, that is the tight accessibility and the strong magnetic field, we adopted a newly designed gold neutral beam probe system including a new type of MCP detector. The characteristics of the MCP detector were obtained successfully using a teststand with strong magnetic field created by the nuclear magnetic resonance (NMR) magnets.This beam probe system was applied to the tandem mirror GAMMA 10, and the electrostatic potential was measured successfully by the beam probe system located in the neighborhood of the IMT region.

A relativistic multiregion bounce-averaged Fokker-Planck code for mirror plasmas