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

In the process of dissipative relaxation, there is strong astrophysical and laboratory evidence that plasmas tend to evolve towards the well-known Woltjer-Taylor state, specified by $\nabla \times \mathit{B}=\alpha \mathit{B}$ for constant $\alpha$. To explain how such a state is reached, Taylor developed his famous theory based on the conjecture that relaxation is dominated by short wavelength fluctuations. However, there is no conclusive experimental or numerical evidence in support of Taylor’s conjecture. A new theory is developed, which predicts that the system will evolve towards the Woltjer-Taylor state for an arbitrary fluctuation spectrum.

Figure 1

Away from a Woltjer-Taylor state, $QW-H^2$ is positive definite and decreasing in time at a nonvanishing rate. Thus, the system is relaxing towards the Woltjer-Taylor state. The state is reached when $QW-H^2=0.$