2 Response to FEAC panel questions

A. What is the current world wide status of research and achievements?

A1. What is the present experimental achievements?

Research is presently being carried out in an ECH heated, mechanically-supported dipole or ``terrella" experiment at Columbia University, the CTX experiment. The CTX provides a test bed for the study of MHD limits and in particular the mechanisms by which hot electron plasmas evolve toward a critical pressure profile. Recent studies [8, 9, 10] demonstrate chaotic radial transport of energetic electrons during strong ECH heating, as would be expected to occur when the pressure gradient exceeds a critical value. The transport is observed directly and simulations support that it derives from multi-mode, drift resonant plasma instabilities. In the afterglow plasma the density is observed to decay quiescently.

With a mechanically-supported dipole, circulating hot electrons are lost when they impact the supports. This creates a loss cone, and plasma confinement is proportional to the pitch-angle scattering rate. The presence of supports provides a significant loss mechanism for the thermal plasma and therefore interferes with studies of cross-field transport. No experiment has ever investigated the confinement of a levitated dipole.

A second class of data in the physics of dipole confinement comes from studies of planetary magnetospheres. In the magnetosphere, transport of magnetically-confined (i.e. energetic) plasma is observed to derive from large scale variations of the magnetic and electric fields that have a time scale on the order of the toroidal precessional frequency, breaking the third adiabatic invariant [11, 12]. Furthermore observations indicate that a stable plasma equilibrium exists with near the equatorial plane in the Jovian magnetosphere [16] which is consistent with MHD calculations.

Levitated ring experiments such as the spherator [17] and levitron [18] have some resemblance to a dipole configuration. The major distinguishing features are as follows:

1. Stability: The proposed dipole is stabilized by flux expansion. This leads to beta values at the stability limit of .

   A spherator or levitron obtains stability from rotational transform in an average minimum-B magnetic configuration and from shear stabilization. MHD typically predicts beta limits of . Drift wave turbulence is present in these devices.

2. Aspect ratio: In terms of the design a dipole experiment requires the wall to be at least 5 ring radii ( ) to permit a sufficient flux expansion. In a levitron the radial build of the TF coils preclude such large radial plasma dimensions and typically .
3. Magnetic topology: The presence of the toroidal and vertical fields in a levitron creates a tokamak-like topology. There is a neo-classical degradation of confinement due to drifts off from the flux surfaces.

   In a dipole the field is poloidal and there is complete axisymmetry (no neo-classical effects).

4. Transport: As in a tokamak, levitron transport was observed to be dominated by drift frequency turbulence while neoclassical effects provides the irreducible minimum. Theoretically, for a dipole, there are no drift frequency wave-plasma interactions and the plasma is stable to low frequency perturbations [1].

A2. What is the present theoretical understanding?

MHD

The equilibrium and ballooning stability has been studied for astrophysical dipoles by several authors. A recent theoretical analysis of ballooning modes in isotropic plasmas has been carried out by Hameiri et al [20]. An analysis has also been done for anisotropic plasmas by Chan et al [21]. In the low beta limit they find that the equilibrium magnetic field is given . Hasegawa estimates that the ballooning limit yields and a more detailed numerical estimate using a self consistent equilibrium yields [21].

Transport

When the critical pressure gradient condition is satisfied in a dipole i.e. , one can show that there are no wave-plasma interactions and the plasma is stable to low frequency perturbations [1]. Higher frequency (cyclotron frequency) drift instability can still be unstable. A recent study by Pastukhov and co-workers [22] indicates that the recycle condition at the internal ring imposes a strong constraint on these modes. He finds that this constraint will limit the magnitude of cyclotron fluctuations and also, as a result, the anomalous heat transport to the ring.

Pressure profiles that violate the critical gradient condition will be subject to instability that broaden the plasma pressure profiles. This is the case for ECH heated plasmas as has been observed in CTX [9]. Non-linear simulations of electrostatic hot electron interchange-type fluctuations are being developed [23]. These simulations are consistent with the CTX results and illustrate the fundamental principles of the dipole concept: fluctuations drive particle distributions towards ``stationary'' profiles that maintain a significant pressure gradient in laboratory coordinates while having a zero gradient in the distribution function in flux-coordinates.

In an astrophysical context, quasilinear models have been used to account for the radial profile of radiation belt particles [24, 25]. Quasilinear and hamiltonian models were compared with CTX experimental transport studies [9, 10].

A3. Does theory, modeling, simulations and empirical scalings fit the experimental observations?

Recent experimental results and modeling performed in the CTX experiment indicates good agreement between theory and experiment on the the unstable relaxation of the pressure profile in a dipole confined plasma toward the critical profile [9, 10, 23]. Measurements of the Jovian atmosphere [16] indicate agreement between theoretical predictions of high beta confinement in dipole fields and the natural occurrence of such plasmas. In addition there is a large body of data on ECR heating in mirror configurations [26].

B. What is the appropriate level of research for this concept?

B1. What are the major experimental and theoretical issues to be addressed.

The major experimental issues are as follows:

1. Explore the ability to produce a high beta hot electron plasmas with substantial stored energy in a levitated dipole configuration. The most direct means to produce a high beta plasma is through the use of ECH. A levitated dipole would eliminate losses to coil supports and since there is no loss cone the only hot electron loss would involve cross-field transport. Questions such as the observed increase in hot electron stored energy obtained with ECR heating at multiple frequencies [26] need to be addressed.

   Study the beta limits of dipole confined hot electron plasmas and the relaxation into the stable state (characterized by a critical pressure gradient). This will follow on to the CTX results discussed above in a more dense and better diagnosed plasma free of loss to supports.

2. Explore the ability to transfer the energy stored in the hot electrons into a thermal plasma. Initially Li pellets could be utilized and ultimately cryogenic hydrogenic pellets would be used. We will determine whether the energy can in fact be transferred into a hydrogenic plasma formed by pellet injection and if this approach extrapolates to a proof-of-principle level experiment.
3. Determine the transport characteristics of the hydrogenic plasma. The dipole holds out the possibility of classical confinement which, if observed, would provide a break-through for fusion research. It is difficult to imagine an accurate assessment of the promise of this concept without a careful research effort devoted to measuring energy confinement and cross field transport. If anomalous transport is observed the degree of this transport will determine the potential for further study.

The major theoretical issues that need to be addressed are the issues surrounding the instability activity that appears as the critical pressure gradient is approached. The manifestation of this limit in a hot electron plasma may prove different than in a thermal plasma.

Detailed solutions of MHD equilibrium at high beta need to be pursued. The development and adoption of predictive tools for ECR heating need to be developed to obtain a predictive capability of the density limits, the energy content and of the power deposition profiles for ECRH in a dipole.

Additionally creative solutions need to be developed for maintaining an internal superconducting ring in a (presumably D- He) fusing plasmas. Dawson's idea [6] of embedding refrigerators within the ring is an example of such an approach.

B2. Do the above issues require launching new experimental facilities and/or theoretical activities?

Yes. Hasegawa first proposed the utilization of the dipole geometry as a fusion confinement approach in 1987. The Columbia CTX experiment has provided interesting and relevant results that support the underlying thesis of the concept, that the pressure profile outside of the ring will self-adjust to the critical profile. It is an appropriate time to build a levitated experiment. Such an experiment will permit the study of stability and confinement in a closed field line dipole system in which plasma losses can only occur across the field lines. The experiment could utilize existing 28 GC gyrotrons, operated continuously at a 10 KW level. A superconducting ring would be designed and built which produces a 1 T field at the desired resonance heating location and it would be levitated in a spherical vacuum tank. In addition, such a system will permit pellet injection and therefore provide the first laboratory facility for the study of the dipole confinement of high beta hydrogenic plasmas.

Simultaneously, we recommend expanding theoretical activities in the areas described above. Although there has not been substantial efforts in this area within the fusion theory community the development of dipole fusion concept should lead to increased interaction between the fusion and space plasma theory communities. Additionally, we recommend the conceptual development of superconducting, levitated coil designs which can function in a fusion environment.

B3. Appropriate mix of research activities

The launching of a new research effort in this area will undoubtedly create interest and activity within the fusion community. The dipole concept is fundamentally different from the presently supported approaches. It both draws on concepts from tokamak, internal ring and mirror confinement research and brings to fore the new issues that arise from the study of the confinement of a plasma in a configuration that has not been previously pursued within the magnetic fusion community.

B4. What is the world-wide research plan?

There is a world-wide and long-standing interest in the confinement properties of the magnetospheric and jovian dipole fields. There has been an interest in internal ring devices in the Russian theory community [22, 27] in the context of appropriate confinement systems for D- He fusion.

B5. Proper Role of US in the context of the international program?

The construction of a small dipole confinement device would place the US in a leadership role in the exploration of this approach. It is certain to attract attention internationally and will be particularly appropriate for collaboration with the Russian (Kurchatov) theory group that has shown interest in this approach.

C1. Potential impact of this concept on increasing out knowledge of general plasma physics.

The potential of this concept for increasing out knowledge of general plasma physics is great. Dipole confinement occurs naturally in nature and results from the simplest possible coil set. The implications for adding understanding of magnetospheric physics is evident.

As discussed above, stability does not rest on the commonly used approach of rotational transform for average well and magnetic shear and is more closely akin to the stability of an absolute minimum-B system. This latter approach may provide the key to the confinement of plasmas at high beta.

Because a dipole creates a particularly simple field structure it also facilitates the possibility of modeling of complex phenomena such as turbulent transport. One could begin studies using the analytic vacuum field geometry. Furthermore the finite beta corrections to the vacuum fields have been shown to be relatively simple [21].

C2. Potential impact of this concept to increase our knowledge of fusion plasma physics.

As stated in the introduction the dipole fundamentally solves the most difficult tokamak problems, i.e. disruptions, divertors, steady state. If we demonstrate the feasibility of storing up substantial energy in a hot electron plasma and then transferring this energy into a dense hydrogenic plasma this would establish a unique and cost effective method for the production of fusion grade laboratory plasmas. Thus the dipole may provide a testing ground for study of fusion grade plasmas under steady state, high beta conditions.

C3. Potential impact of this concept to help develop fusion as an energy source.

Extended burn times in a dipole reactor will require substantial innovation in the design of a self cooled internal superconducting ring. In the shorter term, a shielded dipole coil which remains levitated for relatively short times could provide a laboratory demonstration of short pulses of DT ignition and burning. For example it may be possible to use the stored energy of a hot electron dipole plasma to ignite DT pellets.

C4. Potential impact of this concept for a fusion power plant.

The critical issue for dipole fusion reactor as an energy source remains the feasibility of an internal ring in a fusing plasma. Coupled to this issue is the question of whether a D- He based fusion cycle is realizable from both the point of view of fuel availability and of the associated requirements of confinement and minimized radiation losses.

A major futuristic application of fusion is as an energy source for space propulsion. Teller and co-workers [5] have chosen the dipole as the most promising fusion propulsion configuration, owing largely to the simplicity of the magnetic configuration.