Stability of Plasma Configurations During Compression

Abstract

Magnetized Target Fusion (MTF) efforts are based on calculations showing that the addition of a closed magnetic field configuration reduces the driver pressure and rise time requirements for inertial confinement fusion by reducing thermal conductivity. However, instabilities that result in convective bulk transport at the Alfven time scale are still of concern since they are much faster than the implosion time. Such instabilities may occur during compression due to, for example, an increase in the plasma/magnetic pressure ratio ↓ or, as in the case of a rotating plasma, spin-up due to angular momentum conservation. Details depend on the magnetic field and compression geometries. A hard-core ζ pinch with purely azimuthal magnetic field can theoretically be made that relaxes into a wall supported diffuse profile satisfying the Kadomtsev criterion for the stability of μ = 0 modes, which is preserved during cylindrical compression by an imploding outer return conductor. ↓ at the center conductor surface must also be low enough to stabilize modes with μ ≥ 1. The stability of μ ≥ 1 modes actually improves during compression. A disadvantage of this geometry, though, is plasma contact with the solid boundaries. In addition to the risk of high atomic number impurity contamination during the initial turbulent bulk relaxation process, such contact causes plasma pressure to drop near the outer conductor, violating the Kadomtsev μ = 0 stability criterion locally. The resultant instability can then convect impurities inward. Meanwhile, the center conductor (which is not part of the Kadomtsev profile) can go μ = 0 unstable, convecting impurities outward. One way to mitigate impurity convection is to instead use a Woltjer-Taylor minimum magnetic energy configuration (spheromak). The sheared magnetic field inhibits convection, and the need for a center conductor is eliminated. The plasma, however, would likely still need to be wall supported due to unfavorable ↓ scaling during quasispherical (3D) compression. Use of a Field Reversed Configuration (FRC) substantially resolves the wall contact issue, but at the cost of introducing a new (rotational) instability. An FRC has an open magnetic field outside its separatrix which effectively diverts wall material. However, FRC ions migrating outward across the separatrix have a nonzero average angular momentum, causing the FRC within to counter-rotate in response. When the FRC's rotational/diamagnetic drift frequency ratio → reaches a critical value of order unity, the FRC undergoes a rotational instability resulting in rapid disintegration. The instability is exacerbated by cylindrical compression since → ~P <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2/5</sup> during this phase. A multipole magnetic field frozen into the outer conductor during compression may stabilize this mode directly and/or by impeding spin-up without significantly perturbing the implosion's azimuthal symmetry.