29,785 research outputs found
Numerical study of a nonlinear heat equation for plasma physics
This paper is devoted to the numerical approximation of a nonlinear
temperature balance equation, which describes the heat evolution of a
magnetically confined plasma in the edge region of a tokamak. The nonlinearity
implies some numerical difficulties, in particular long time behavior, when
solved with standard methods. An efficient numerical scheme is presented in
this paper, based on a combination of a directional splitting scheme and the
IMEX scheme introduced in [Filbet and Jin
Solar wind collisional heating
To properly describe heating in weakly collisional turbulent plasmas such as
the solar wind, inter-particle collisions should be taken into account.
Collisions can convert ordered energy into heat by means of irreversible
relaxation towards the thermal equilibrium. Recently, Pezzi et al. (Phys. Rev.
Lett., vol. 116, 2016, p. 145001) showed that the plasma collisionality is
enhanced by the presence of fine structures in velocity space. Here, the
analysis is extended by directly comparing the effects of the fully nonlinear
Landau operator and a linearized Landau operator. By focusing on the relaxation
towards the equilibrium of an out of equilibrium distribution function in a
homogeneous force-free plasma, here it is pointed out that it is significant to
retain nonlinearities in the collisional operator to quantify the importance of
collisional effects. Although the presence of several characteristic times
associated with the dissipation of different phase space structures is
recovered in both the cases of the nonlinear and the linearized operators, the
influence of these times is different in the two cases. In the linearized
operator case, the recovered characteristic times are systematically larger
than in the fully nonlinear operator case, this suggesting that fine velocity
structures are dissipated slower if nonlinearities are neglected in the
collisional operator
Optimisation of confinement in a fusion reactor using a nonlinear turbulence model
The confinement of heat in the core of a magnetic fusion reactor is optimised
using a multidimensional optimisation algorithm. For the first time in such a
study, the loss of heat due to turbulence is modelled at every stage using
first-principles nonlinear simulations which accurately capture the turbulent
cascade and large-scale zonal flows. The simulations utilise a novel approach,
with gyrofluid treatment of the small-scale drift waves and gyrokinetic
treatment of the large-scale zonal flows. A simple near-circular equilibrium
with standard parameters is chosen as the initial condition. The figure of
merit, fusion power per unit volume, is calculated, and then two control
parameters, the elongation and triangularity of the outer flux surface, are
varied, with the algorithm seeking to optimise the chosen figure of merit. A
two-fold increase in the plasma power per unit volume is achieved by moving to
higher elongation and strongly negative triangularity.Comment: 32 pages, 8 figures, accepted to JP
Can conduction induce convection? The non-linear saturation of buoyancy instabilities in dilute plasmas
We study the effects of anisotropic thermal conduction on low-collisionality,
astrophysical plasmas using two and three-dimensional magnetohydrodynamic
simulations. For weak magnetic fields, dilute plasmas are buoyantly unstable
for either sign of the temperature gradient: the heat-flux-driven buoyancy
instability (HBI) operates when the temperature increases with radius while the
magnetothermal instability (MTI) operates in the opposite limit. In contrast to
previous results, we show that, in the presence of a sustained temperature
gradient, the MTI drives strong turbulence and operates as an efficient
magnetic dynamo (akin to standard, adiabatic convection). Together, the
turbulent and magnetic energies contribute up to ~10% of the pressure support
in the plasma. In addition, the MTI drives a large convective heat flux, ~1.5%
of rho c_s^3. These findings are robust even in the presence of an external
source of strong turbulence. Our results on the nonlinear saturation of the HBI
are consistent with previous studies but we explain physically why the HBI
saturates quiescently by re-orienting the magnetic field (suppressing the
conductive heat flux through the plasma), while the MTI saturates by generating
sustained turbulence. We also systematically study how an external source of
turbulence affects the saturation of the HBI: such turbulence can disrupt the
HBI only on scales where the shearing rate of the turbulence is faster than the
growth rate of the HBI. In particular, our results provide a simple mapping
between the level of turbulence in a plasma and the effective isotropic thermal
conductivity. We discuss the astrophysical implications of these findings, with
a particular focus on the intracluster medium of galaxy clusters.Comment: 18 pages, 14 figures. Submitted to MNRA
Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability
In collisionless and weakly collisional plasmas, such as hot accretion flows
onto compact objects, the magnetorotational instability (MRI) can differ
significantly from the standard (collisional) MRI. In particular, pressure
anisotropy with respect to the local magnetic-field direction can both change
the linear MRI dispersion relation and cause nonlinear modifications to the
mode structure and growth rate, even when the field and flow perturbations are
small. This work studies these pressure-anisotropy-induced nonlinearities in
the weakly nonlinear, high-ion-beta regime, before the MRI saturates into
strong turbulence. Our goal is to better understand how the saturation of the
MRI in a low collisionality plasma might differ from that in the collisional
regime. We focus on two key effects: (i) the direct impact of self-induced
pressure-anisotropy nonlinearities on the evolution of an MRI mode, and (ii)
the influence of pressure anisotropy on the "parasitic instabilities" that are
suspected to cause the mode to break up into turbulence. Our main conclusions
are: (i) The mirror instability regulates the pressure anisotropy in such a way
that the linear MRI in a collisionless plasma is an approximate nonlinear
solution once the mode amplitude becomes larger than the background field (just
as in MHD). This implies that differences between the collisionless and
collisional MRI become unimportant at large amplitudes. (ii) The break up of
large amplitude MRI modes into turbulence via parasitic instabilities is
similar in collisionless and collisional plasmas. Together, these conclusions
suggest that the route to magnetorotational turbulence in a collisionless
plasma may well be similar to that in a collisional plasma, as suggested by
recent kinetic simulations. As a supplement to these findings, we offer
guidance for the design of future kinetic simulations of magnetorotational
turbulence.Comment: Submitted to Journal of Plasma Physic
Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions
We study the anomalous dynamical scaling of equilibrium correlations in one
dimensional systems. Two different models are compared: the Fermi-Pasta-Ulam
chain with cubic and quartic nonlinearity and a gas of point particles
interacting stochastically through the multiparticle collision dynamics. For
both models -that admit three conservation laws- by means of detailed numerical
simulations we verify the predictions of nonlinear fluctuating hydrodynamics
for the structure factors of density and energy fluctuations at equilibrium.
Despite this, violations of the expected scaling in the currents correlation
are found in some regimes, hindering the observation of the asymptotic scaling
predicted by the theory. In the case of the gas model this crossover is clearly
demonstrated upon changing the coupling constant.Comment: 12 pages, 8 figures. Matching the version published in Phys. Rev.
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