Håkan Smith

Hot tail runaway electron generation in tokamak disruptions

Hot tail runaway electron generation is caused by incomplete thermalization of the electron velocity distribution during rapid plasma cooling. It is an important runaway electron mechanism in tokamak disruptions if the thermal quench phase is sufficiently fast. Analytical estimates of the density of produced runaway electrons are derived for cases of exponential-like temperature decay with a cooling rate lower than the collision frequency. Numerical simulations, aided by the analytical results, are used to compare the strength of the hot tail runaway generation with the Dreicer mechanism for different disruption parameters (cooling rate, post-thermal quench temperature, and electron density) assuming that no losses of runaway electrons occur. It is seen that the hot tail runaway production is going to be the dominant of these two primary runaway mechanisms in ITER [R. Aymar et al., Plasma Phys. Controlled Fusion 44, 519 (2002)].

Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas

In this work, we examine the validity of several common simplifying assumptions used in numerical neoclassical calculations for nonaxisymmetric plasmas, both by using a new continuum drift-kinetic code and by considering analytic properties of the kinetic equation. First, neoclassical phenomena are computed for the LHD and W7-X stellarators using several versions of the drift-kinetic equation, including the commonly used incompressible-E × B-drift approximation and two other variants, corresponding to different effective particle trajectories. It is found that for electric fields below roughly one third of the resonant value, the different formulations give nearly identical results, demonstrating the incompressible E × B-drift approximation is quite accurate in this regime. However, near the electric field resonance, the models yield substantially different results. We also compare results for various collision operators, including the full linearized Fokker-Planck operator. At low collisionality, the radial transport driven by radial gradients is nearly identical for the different operators; while in other cases, it is found to be important that collisions conserve momentum.

Recent experiments on Alfvén eigenmodes in MAST

The developments of advanced tokamak scenarios as well as the employment of a new neutral beam injection (NBI) source with higher power and beam energy up to ≈65keV have significantly broadened the frequency range and the variety of Alfv´ en eigenmodes (AEs) excited by the super-Alfv´ enic NBI on the spherical tokamak MAST. During recent experiments on MAST, several distinct classes of beam-driven AEs have been identified, with different modes being most unstable in different MAST scenarios. In MAST discharges with elevated monotonic q(r)-profiles and NBI power 3MW, chirping modes starting in the frequency range 150kHz decreased in frequency down to ≈20kHz as q(0) decreased and then smoothly transformed to long-living modes with a weakly-varying frequency and a n = 1 kink-mode structure. The bolometer data suggest that the long-living modes can be responsible for fast ion losses on MAST, while the charge-exchange data show that a coupling between these modes and other low-frequency modes can cause a collapse of toroidal plasma rotation with a subsequent disruption. In MAST

Runaway electrons and the evolution of the plasma current in tokamak disruptions

After the thermal quench of a tokamak disruption, the plasma current decays and is partly replaced by runaway electrons. A quantitative theory of this process is presented, where the evolution of the toroidal electric field and the plasma current is calculated self-consistently. In large tokamaks most runaways are produced by the secondary (avalanche) mechanism, but the primary (Dreicer) mechanism plays a crucial role in providing a “seed” for the avalanche. As observed experimentally, up to 50%–60% of the plasma current is converted into runaways in the Joint European Torus [P. H. Rebut et al., Nucl. Fusion 25, 1011 (1985)], and the conversion is predicted to be somewhat larger in ITER [R. Aymar et al., Plasma Phys. Controlled Fusion 44, 519 (2002)]. Furthermore, the postdisruption current profile is found to be more peaked than the predisruption current—so much, in fact, that the central current density can increase although the total current falls. It is also found that the runaway current profile easi...

Runaway electron generation in a cooling plasma

The usual calculation of Dreicer [Phys. Rev. 115, 238 (1959); 117, 329 (1960)] generation of runaway electrons assumes that the plasma is in a steady state. In a tokamak disruption this is not necessarily true since the plasma cools down quickly and the collision time for electrons at the runaway threshold energy can be comparable to the cooling time. The electron distribution function then acquires a high-energy tail which can easily be converted to a burst of runaways by the rising electric field. This process is investigated and simple criteria for its importance are derived. If no rapid losses of fast electrons occur, this can be a more important source of runaway electrons than ordinary Dreicer generation in tokamak disruptions.

Magnetic field threshold for runaway generation in tokamak disruptions

Experimental observations show that there is a magnetic field threshold for runaway electron generation in tokamak disruptions. In this work, two possible reasons for this threshold are studied. The first possible explanation for these observations is that the runaway beam excites whistler waves that scatter the electrons in velocity space prevents the beam from growing. The growth rates of the most unstable whistler waves are inversely proportional to the magnetic field strength. Taking into account the collisional and convective damping of the waves it is possible to derive a magnetic field threshold below which no runaways are expected. The second possible explanation is the magnetic field dependence of the criterion for substantial runaway production obtained by calculating how many runaway electrons can be produced before the induced toroidal electric field diffuses out of the plasma. It is shown, that even in rapidly cooling plasmas, where hot-tail generation is expected to give rise to substantial runaway population, the whistler waves can stop the runaway formation below a certain magnetic field unless the postdisruption temperature is very low.

Compressional Alfven Eigenmodes on MAST

Magnetic fluctuations at frequencies ω ωci driven by neutral-beam injection heating and identified as compressional Alfven eigenmodes (CAEs) have been observed on MAST. The measured toroidal mode numbers are in the range 4 < |n| < 10 and waves rotate in both co- and counter-current directions. The frequency variation is consistent with an Alfvenic scaling, and modes are elliptically polarized with a significant magnetic field component aligned parallel to the equilibrium field. Frequency clustering of modes occurs on three frequency scales. At the finest scale there are multiple modes each separated by a constant frequency ~10–20 kHz; this is shown to be a result of modulation by low-frequency tearing modes. A larger scale frequency splitting exists in the range 100–150 kHz; these have consecutive toroidal mode numbers and are in agreement with numerical modelling. Finally, modes exist at frequencies close to ω = ωci and ωci/2 consistently with previous observations on START and DIII-D suggesting that the CAEs exist in two distinct ranges of k∥. Calculations of CAEs suggest that the modes are localized at r/a ~ 0.5. The modes form within a potential well due to the variation of (nq/κρ)2, and are not directly influenced by variations in vA. This is distinct from observations based on ion cyclotron emission in conventional aspect ratio tokamaks which indicate that CAE modes occur closer to the plasma edge and that their existence relies on a competition between k⊥ and 1/vA.

Simulation of runaway electron generation during plasma shutdown by impurity injection in ITER

Disruptions in a large tokamak can cause serious damage to the device and should be avoided or mitigated. Massive gas or killer pellet injection are possible ways to obtain a controlled fast plasma shutdown before a natural disruption occurs. In this work, plasma shutdown scenarios with different types of impurities are studied for an ITER-like plasma. Plasma cooling, runaway generation and the associated electric field diffusion are calculated with a 1D-code taking the Dreicer, hot-tail and avalanche runaway generation processes into account. Thin, radially localized sheets with high temperature can be created after the thermal quench, and the Dreicer and avalanche processes produce a high runaway current inside these sheets. At high impurity concentration the Dreicer process is suppressed but hot-tail runaways are created. Favorable thermal and current quench times can be achieved with a mixture of deuterium and neon or argon. However, to prevent the avalanche process from creating a significant runaway current fraction, it is found to be necessary to include runaway losses in the model.

Runaway electron generation in tokamak disruptions

Runaway electrons can be generated in disruptions by the Dreicer, hot tail and avalanche mechanisms. Analytical and numerical results for hot tail runaway generation are included in a one-dimensional model of electric field, temperature and runaway current, which is applied to simulate disruptions and fast shutdown. The peaked shape of the runaway current density profile may cause tearing modes to become unstable. Fast shutdown is studied by prescribing varying amounts of injected impurities. Large argon content suppresses runaways in JET simulations but causes hot tail generation in ITER. A pellet code is coupled to the runaway model, and it is extended to enable simulations of carbon doped deuterium pellet injection. Such pellets are seen not to give enough cooling for a fast current quench.

A model for falling‐tone chorus

Motivated by the fact that geomagnetic field inhomogeneity is weak close to the chorus generation region and the observational evidence that falling-tone chorus tend to have large oblique angles of propagation, we propose that falling-tone chorus start as a marginally unstable mode. The marginally unstable mode requires the presence of a relatively large damping, which has its origins in the Landau damping of oblique waves in this collisionless environment. A marginally unstable mode produces phase-space structures that release energy and produce wave chirping. We show that the present model produces results in reasonable agreement with observations.