Woltjer-Taylor State without Taylor’s Conjecture: Plasma Relaxation at all Wavelengths

Qinet al.Reply:

“…For this solution,ẋ = 0 for all x as t → ∞, contradicting the property that∆ = 0 if and only if ∆ = 0 as proved in [2]. The smoothness of functions will ensure that if∆ is very small, then ∆ is also, i.e., the system is very close to the Woltjer-Taylor (WT) state.…”

“…(27) of [2] is that the total magnetic energy variation is primarily due to resistive dissipation. There is no stipulation that plasma dynamics at each individual wavelength must be dominated by resistive decay, and indeed this will not be true in all but the most simple cases due to the strongly nonlinear behavior of the plasma.…”

“…To emphasize these nonlinear characteristics and to further rule out the possibility of ∆ decaying at the same rate as H 2 , we would like to refine the physical picture presented in [2].…”

Exact axisymmetric Taylor states for shaped plasmas

“…For equilibria with a magnetic X-point, the location of the X-point must also be specified. The flexibility and simplicity of these solutions make them useful for verifying the accuracy of numerical solvers and for theoretical studies of Taylor states in laboratory experiments.Plasmas in both astrophysical and laboratory settings have a strong tendency to relax to minimum energy states known as Taylor states or Woltjer-Taylor states [1][2][3][4][5][6][7][8][9][10][11][12] in which the magnetic fields are force-free fields given by the equationwhere λ is a global constant. A well-known analytic solution to equation (1) is often used for theoretical studies and to interpret experiments [5][6][7]13 .…”

“…Plasmas in both astrophysical and laboratory settings have a strong tendency to relax to minimum energy states known as Taylor states or Woltjer-Taylor states [1][2][3][4][5][6][7][8][9][10][11][12] in which the magnetic fields are force-free fields given by the equation…”