ª 10 KeV. In 2XIIB and the tandem mirrors built to date, in which the plug radius R p. ª r Li

Transcription

1 Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies R. F. Post, T. K. Fowler*, R. Bulmer, J. Byers, D. Hua, L. Tung Lawrence Livermore National Laboratory *Consultant, Presenter This talk will present some new results for the kinetically-stabilized tandem mirror, which offers exciting improvements compared to tandem mirrors of the 1980 s. To put this in context, we first review the original tandem mirror concept successfully demonstrated in TMX at LLNL and elsewhere. Viewgraph 1 shows the original tandem mirror concept with yin yang end plugs (no thermal barriers). Fusion power would be produced in the simple solenoidal center cell. Neutral beam injection in the plugs produces potentials that confine ions in the center cell by the formulas shown. The potential confining the ions is proportional to T e, so the key to high end-plug potentials is electron temperatures much higher than those achieved in mirrors to date. We believe this is understood. High potentials expel low energy plug ions, which causes various ion cyclotron instabilities, as was demonstrated and then controlled in the highly successful 2XIIB yin-yang mirror experiment in the mid 1970 s, with b ª 1 and T i ª 10 KeV. In 2XIIB and the tandem mirrors built to date, in which the plug radius R p ª r Li (the plug ion Larmor radius), stability required replacing the cold ions by plasma streaming through the mirror, supplied by center cell end losses in the case of tandem mirrors. This flow predictably cooled T e to about 1% of the neutral beam energy. According to theory, the path to a reactor with negligible end losses is high field plugs giving R p /r Li >> 1, in which case no streaming is required. As end loss was progressively reduced in tandem mirrors, it was also found that ion radial transport began to limit lifetimes, again yielding low electron temperatures. The joining of yin-yangs to the solenoid was known to contribute to this radial transport. Viewgraph 2 shows a flux surface for a symmetric tandem mirror with high field circular coils in the end plugs, with kinetic stabilizer injectors to maintain MHD stability. This configuration, inspired by success with the Gas Dynamic Trap at Novosibirsk, is expected to produce much less radial transport, and the now-demonstrated technical feasibility of very high field plugs with small non-superconducting circular coils consuming little power offers a cost-effective way of achieving high R p /r Li >> 1 needed to suppress ion cyclotron modes as discussed above. In the Gas Dynamic Trap, overall MHD stability is achieved by counterbalancing unstable plugs by pressure of escaping plasma on the fans with good field line curvature. This outflow again cools the electrons. The Kinetic

2 Stabilizer avoids electron cooling by supplying pressure in the fans by injecting low energy ions that reflect from the mirrors before reaching the plug plasma. Viewgraph 3 shows results from Gas Dynamic Trap experiments in which energetic ions trapped in the center cell reached b = 40% with no evidence of instability or measurable radial transport. Viewgraph 4 shows the familiar theoretical condition for ideal MHD stability, in terms of an integral of b along field lines, weighted by the curvature and pressure gradient length (essentially the radius a of the outer flux surface). Viewgraph 5 applied this formula to equilibria produced by the FLORA MHD code with two conditions for kinetic stabilizer beam injection producing the beta profiles shown in Cases A and B. The peaks to the left correspond to the unstable plug plasmas, while the distributions to the right represent the stabilizer beam ions. Different beam beta profiles correspond to different angles of injection and spreads of the angles. Both cases are stable by the criteria of Viewgraph 4, and both yield b = 40% in the plugs. Viewgraph 6 shows the actual pressure profiles for Case A, scaled to 1 in the plugs. The stabilizer beam pressure is about 1000 times less than the plug pressure, and the ratio of energies stored in the plug and stabilizer (roughly equal to the ratio of fields) is also On the other hand, the lifetime of stabilizer ions (just their bounce time) is much shorter, so that for typical 1 KeV Cs stabilizer beams the power to maintain the stabilizer is comparable to that required to maintain the plugs (lifetime ª 0.1 s), both being much less than the fusion power produced in center cells of moderate length < 100 m. Of course, cold plasma is required to provide conduction between the stabilizer and plug, which adds to cooling of the hot plasmas and possibly causes trapped particle modes. Estimates indicate that trapped particle growth rates begin to be suppressed at densities about 10-4 times the center cell density (a negligible heat load). More work is needed to understand trapped particle modes in the kinetically-stabilized symmetric tandem mirror. Viewgraph 7 shows results of confinement in a tandem mirror reactor center cell, using the SYMTRAN code with 1-D radial transport and formulas to represent end losses with self-consistently calculated potentials (assuming high field plugs stable to ion cyclotron modes as discussed above). Radial transport of the ions is assumed to be classical, based on success in tokamaks whereby ITG modes are stabilized by electric field shear. Electric field stabilization can more easily be achieved in a tandem mirror, utilizing the natural potential and voltages applied to segmented end plates to shape the profile as needed to stabilize both ITG and rotational modes. The code does include anomalous electron heat transport, in gyrobohm form to represent ETG modes that are one candidate for residual electron anomalous transport in tokamaks. Even so, an electron temperature of 80

3 KeV and a fusion power gain Q = 10 has been obtained, not yet optimized. Here B = 3 T and R (solenoid radius) = 1 m, giving BR = 3 (comparable to that for the poloidal field in ITER but << BR = 15 for the toroidal field). Note that these results were obtained using the original concept for end plugging, demonstrated in TMX, that did not require thermal barriers. Viewgraph 8 reviews the necessity for and limitations on high electron temperatures in the original tandem mirror. The maximum achievable T e = 10% of the plug ion energy implies 1 MeV beams in the plugs, now the goal of neutral beams for ITER. The beam power requirement is also similar to that for ITER. Viewgraph 9 shows theoretical requirements on R p /r Li to stabilize the plugs against the Drift Cyclotron Loss Cone mode (DCLC) thought to be the limiting process. The upper curve corresponds to no streaming of warm plasma n W through the plugs, the goal for a reactor. The value of R p /r Li required for stability depends on the plug density, through the ion plasma frequency w pi. At very low density, R p /r Li can be unity, demonstrated in stable BBII experiments that did achieve T e = 10% of the plug ion energy for 1 and 2 KeV beams. Reactors require R p /r Li > 40 in the plug, which yields BR = 3 in the center cell assumed in Viewgraph 7. A convincing experimental test could be obtained with plugs of lower density and R p /r Li = 10. Viewgraph 10 summarizes our results: namely, kinetically-stabilized high-field symmetric plugs offer a superior path to steady-state tandem-mirror fusion power systems. The key issues (kinetic stabilization, plug stability) could be tested in modest facilities. For example, high field plugs in a device like Gamma 10 could perhaps achieve T e = 1 KeV, well beyond previous results in mirror devices.

4 Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies Innovative Confinement Concepts Workshop May , Madison, Wisconsin R. F. Post, T. K. Fowler*, R. Bulmer, J. Byers, D. Hua, L. Tung Lawrence Livermore National Laboratory *Consultant, Presenter ICC-04-01

5 Original Tandem Mirror Concept Neutral beams Neutral beams Flux surface Potential Confinement: Center cell: È f i = T e lní Î È n(z) = n 0 exp f Í Î T e n plug n center cell È t E = t ii exp f i Í Î T i ICC-04-02

6 Flux surfaces in the Kinetically Stabilized tandem mirror are much simpler than the original tandem mirror Expander Central mirror cell (end) Kinetic Stabilizer injectors Plug mirror cell ICC-03-03

7 Kinetic stabilization is based on physics proved in the Gas Dynamic Trap* GDT Parameters Mirror-to-mirror distance 7.0 m. Magnetic field: at midplane 0.28 T in mirrors T Target plasma density 3-20x10 20 m -3 Electron temperature up to 130 ev Density of fast ions about m -3 Mean energy of fast ions 8-10 kev Maximal plasma b 40 % * A. A. Ivanov, et. al. Trans. Fusion Science and Technology, 43, 51 (2003) ICC-04-04

8 The criterion for MHD stability of plasma confined in an axisymmetric mirror system is given by theory I = L a 3 d 2 a Ú dz 2 p^ + p II + rv 2 -L [ ] dz > 0, Stable or I µ b Ú dz > 0, Stable ar c a = radius of plasma boundary L = axial boundary of plasma R c = radius of curvature of line of force ICC-04-05

9 The FLORA MHD code predicts b = 40% in the plugs: Examples for two injection conditions Case A b Z(cm) Case B b Z(cm) ICC-04-06

10 Pressure profiles for Case A (Normalized to plug midplane) p^ Stabilizer p Z(cm) p^ Plug p Z(cm) ICC-04-07

11 Example reactor parameters including radial transport (ignited center cell with classical and ETG transport) T e T i kev T e T i Time (sec.) r/r Initial results from thesymtran 1-D radial-transport code with symmetric tandem mirror end losses (D. Hua and T. K. Fowler, 5/7/04) ICC=04-08

12 A symmetric tandem-mirror fusion power system requires high electron temperature High electron temperatures are possible only with end plugs stable to ion-cyclotron modes (DCLC). The maximum electron temperature is about 10% of the plug ion energy. This result has been achieved in low-density stable mirror machines. ICC-04-09

13 End plug stability at high density is possible with high-field plugs (large R p /r Li ) DCLC stability boundaries (D. E. Baldwin, RMP 49, 317 (1977) Reactor High-field experiment BB II ICC-04-10

14 Summary High-field, symmetric plugs offer a superior path to a steady-state tandem-mirror fusion power systems Key issues (Kinetic Stabilizer, plug stability) could be tested in modest facilities employing high-field plugs ICC-04-11