Energy confinement and magnetic field generation in the SSPX spheromak Page: 4 of 31
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I. Introduction
A spheromak [1] plasma is formed by injecting magnetic helicity, K =fvAeBdV, whereA
is the magnetic vector potential, into an axisymmetric flux conserver. During injection, the
magnetic field lines, bent from the vacuum configuration in the flux conserver and the pinching
of the current that drives the injection, reconnect and form closed axisymmetric surfaces. During
spheromak formation with a coaxial plasma gun, the current flowing along field lines inside the
flux conserver drives an n = 1 instability on the open flux down the geometric axis (sometimes
referred to as the "dough-hook"[2,3,4] mode) which drives magnetic reconnection and builds
magnetic field but inhibits the formation of nested magnetic surfaces. If gun current is then
reduced below the n = 1 instability threshold, the plasma evolves close to the so-called "Taylor
state"[5] in which the plasma currents and magnetic fields reorganize themselves to reach a
minimum energy configuration and axisymmetric flux surfaces form. This configuration is
characterized by a flat or nearly flat parallel current profile, ) = poJl / B = constant. Best energy
confinement is found for a profile which is slightly peaked on the magnetic axis, resulting in a q-
profile which lies in the range 1/2 < q(4') < 2/3 except near the separatrix, thereby eliminating
low-order rational surfaces in the plasma [9]. An additional consequence of ) ~ constant is
that it limits the drive for resistive tearing modes, which both take energy from the field itself
and leads to stochastic field lines and parallel energy transport. Maintaining current on the open
flux also maintains the plasma for an extended period of time and delays the onset of a
destructive n = 2 (toroidal) mode caused by decay of the current near the wall which would lead
to a decrease of the safety-factor at the edge below q = 1/2.
One of the most important goals of spheromak research is to understand how to build
closed equilibria and sustain a stable discharge long enough for Ohmic heating to heat the2 of 29
V.11
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Hudson, B.; McLean, H. S.; Wood, R. D.; Hooper, E. B.; Hill, D. N.; Jayakumar, J. et al. Energy confinement and magnetic field generation in the SSPX spheromak, article, February 11, 2008; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc897283/m1/4/: accessed July 15, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.