A nonlinear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma by Rosin, MS, Schekochihin, A, Rincon, F, Cowley, S

“…In the nonlinear regime, both analytical theory and the numerical solution predict secular growth of magnetic fluctuations. They develop a k^{-3} spectrum, extending from scales somewhat larger than \rho_i to the maximum scale that grows secularly with time (~t^{1/2}); the relative pressure anisotropy (\pperp-\ppar)/\ppar tends to the marginal value -2/\beta_i. …”

A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma by Rosin, MS, Schekochihin, A, Rincon, F, Cowley, S

“…In the non-linear regime, both the analytical theory and the numerical solution predict secular (∝t) growth of magnetic fluctuations. The fluctuations develop a k {double pipe}-3 spectrum, extending from scales somewhat larger than ρ i to the maximum scale that grows secularly with time (∝t 1/2); the relative pressure anisotropy (p ⊥ - p {double pipe})/p {double pipe} tends to the marginal value -2/β i. …”

Nonlinear growth of firehose and mirror fluctuations in astrophysical plasmas. by Schekochihin, A, Cowley, S, Kulsrud, R, Rosin, MS, Heinemann, T

“…The principle of their nonlinear evolution is to generate secularly growing small-scale magnetic fluctuations that on average cancel the temporal change in the large-scale magnetic field responsible for the pressure anisotropies. …”

Nonlinear mirror instability by Rincon, F, Schekochihin, A, Cowley, S

“…Instead, the trapping of particles in small-scale mirrors leads to nonlinear secular growth of magnetic perturbations, $\delta B/B \propto t^{2/3}$. …”

Firehose and Mirror Instabilities in a Collisionless Shearing Plasma by Kunz, M, Schekochihin, A, Stone, J

“…In contrast, nonlinear mirror fluctuations are large compared to the ion Larmor scale and grow secularly in time; marginality is maintained by an increasing population of resonant particles trapped in magnetic mirrors. …”

Thermal conduction in a mirror-unstable plasma by Komarov, S, Churazov, E, Kunz, M, Schekochihin, A

“…We find suppression down to ≈0.2 of the Spitzer value for the secular phase of the perturbations’ growth, and ≈0.3 for their saturated phase. …”

Pressure-anisotropy-driven microturbulence and magnetic-field evolution in shearing, collisionless plasma by Melville, S, Schekochihin, A, Kunz, M

“…In this regime, driven firehose fluctuations grow secularly to order-unity amplitudes, compensating for the decay of the mean field and so pinning pressure anisotropy at marginal stability with no appreciable scattering of particles---which is unlike what happens at moderate $\beta$. …”