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Register a new userEquations and improved coefficients for paralleltransport in multicomponent collisional plasmas: method and application for tokamak modelling
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New analytical expressions for parallel transport coefficients in multicomponent collisional plasmas are presented in this paper. They are improv
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In large hot tokamaks like JET, the width of the reconnecting layer for resistive modes is determined by semi-collisional electron dynamics and is much less than the ion Larmor radius. Firstly a dispersion relation valid in this regime is derived which provides a unified description of drift-tearing modes, kinetic Alfven waves and the internal kink mode at low beta. Tearing mode stability is investigated analytically recovering the stabilising ion orbit effect, obtained previously by Cowley et al. [Phys. Fluids (29) 3230 1986], which implies large values of the tearing mode stability parameter Delta prime are required for instability. Secondly, at high beta it is shown that the tearing mode interacts with the kinetic Alfven wave and that there is an absolute stabilisation for all Delta prime due to the shielding effects of the electron temperature gradients, extending the result of Drake et. al [Phys. Fluids (26) 2509 1983] to large ion orbits. The nature of the transition between these two limits at finite values of beta is then elucidated. The low beta formalism is also relevant to the m=n=1 tearing mode and the dissipative internal kink mode, thus extending the work of Pegoraro et al. [Phys. Fluids B (1) 364 1989] to a more realistic electron model incorporating temperature perturbations, but then the smallness of the dissipative internal kink mode frequency is exploited to obtain a new dispersion relation valid at arbitrary beta. A diagram describing the stability of both the tearing mode and dissipative internal kink mode, in the space of Delta prime and beta, is obtained. The trajectory of the evolution of the current profile during a sawtooth period can be plotted in this diagram, providing a model for the triggering of a sawtooth crash.
It is shown that rapid substantial changes in heating rate can induce transitions to improved energy confinement regimes in zero-dimensional models for tokamak plasma phenomenology. We examine for the first time the effect of step changes in heating rate in the models of E-J.Kim and P.H.Diamond, Phys.Rev.Lett. 90, 185006 (2003) and M.A.Malkov and P.H.Diamond, Phys.Plasmas 16, 012504 (2009) which nonlinearly couple the evolving temperature gradient, micro-turbulence and a mesoscale flow; and in the extension of H.Zhu, S.C.Chapman and R.O.Dendy, Phys.Plasmas 20, 042302 (2013), which couples to a second mesoscale flow component. The temperature gradient rises, as does the confinement time defined by analogy with the fusion context, while micro-turbulence is suppressed. This outcome is robust against variation of heating rise time and against introduction of an additional variable into the model. It is also demonstrated that oscillating changes in heating rate can drive the level of micro-turbulence through a period-doubling path to chaos, where the amplitude of the oscillatory component of the heating rate is the control parameter.
We discuss the role of neoclassical resistivity and local magnetic shear in the triggering of the sawtooth in tokamaks. When collisional detrapping of electrons is considered the value of the safety factor on axis, $q(0,t)$, evolves on a new time scale, $tau_{*}=tau_{eta} u_{*}/(8sqrt{epsilon})$, where $tau_{eta}=4pi a^{2}/[c^{2}eta(0)]$ is the resistive diffusion time, $ u_{*}= u_{e}/(epsilon^{3/2}omega_{te})$ the electron collision frequency normalised to the transit frequency and $epsilon=a/R_{0}$ the tokamak inverse aspect ratio. Such evolution is characterised by the formation of a structure of size $delta_{*}sim u_{*}^{2/3}a$ around the magnetic axis, which can drive rapid evolution of the magnetic shear and decrease of $q(0,t)$. We investigate two possible trigger mechanisms for a sawtooth collapse corresponding to crossing the linear threshold for the $m=1,n=1$ instability and non-linear triggering of this mode by a core resonant mode near the magnetic axis. The sawtooth period in each case is determined by the time for the resistive evolution of the $q$-profile to reach the relevant stability threshold; in the latter case it can be strongly affected by $ u_*.$
The effect of momentum injection on the temperature gradient in tokamak plasmas is studied. A plausible scenario for transitions to reduced transport regimes is proposed. The transition happens when there is sufficient momentum input so that the velocity shear can suppress or reduce the turbulence. However, it is possible to drive too much velocity shear and rekindle the turbulent transport. The optimal level of momentum injection is determined. The reduction in transport is maximized in the regions of low or zero magnetic shear.
The physical foundations of the dissipation of energy and the associated heating in weakly collisional plasmas are poorly understood. Here, we compare and contrast several measures that have been used to characterize energy dissipation and kinetic-scale conversion in plasmas by means of a suite of kinetic numerical simulations describing both magnetic reconnection and decaying plasma turbulence. We adopt three different numerical codes that can also include interparticle collisions: the fully kinetic particle-in-cell VPIC, the fully kinetic continuum Gkeyll, and the Eulerian Hybrid Vlasov-Maxwell (HVM) code. We differentiate between (i) four energy-based parameters, whose definition is related to energy transfer in a fluid description of a plasma, and (ii) four distribution function-based parameters, requiring knowledge of the particle velocity distribution function. There is an overall agreement between the dissipation measures obtained in the PIC and continuum reconnection simulations, with slight differences due to the presence/absence of secondary islands in the two simulations. There are also many qualitative similarities between the signatures in the reconnection simulations and the self-consistent current sheets that form in turbulence, although the latter exhibits significant variations compared to the reconnection results. All the parameters confirm that dissipation occurs close to regions of intense magnetic stresses, thus exhibiting local correlation. The distribution function-based measures show a broader width compared to energy-based proxies, suggesting that energy transfer is co-localized at coherent structures, but can affect the particle distribution function in wider regions. The effect of interparticle collisions on these parameters is finally discussed.
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