The lifetime of pre-existing runaway electrons determines how likely the runaways will undergo avalanche multiplication. We estimate the lifetime of runaway electrons via kinetic analysis. We show that the rate of runaway decay depends on the combination of parameters α≡(Z+1)/τ¯rad (where τ¯rad is the synchrotron timescale normalized to the collisional timescale and Z is the ion charge) compared to the electric field. We identify two cases where the decay rate is slow enough to enable a quasi-steady shape of the runaway distribution function. This distribution and its lifetime represent the eigenfunction and the lowest eigenvalue of the kinetic equation. In one case, α≪1: the field required to sustain the pre-existing runaways is barely larger than the Connor-Hastie critical value. In the same manner as by Aleynikov and Breizman [Phys. Rev. Lett. 114, 155001 (2015)], we solve the kinetic equation perturbatively but extend the work to demonstrate that the lifetime grows exponentially with the field at a rate that depends on α. In the second case, α≫1: the sustainment field is much greater than the Connor-Hastie value, and the largeness of the field in this case enables us to universalize the kinetic equation via the re-scaling procedure.
Alfvén eigenmodes driven by energetic particles are routinely observed in tokamak plasmas. These modes consist of poloidal harmonics of shear Alfvén waves coupled by inhomogeneity in the magnetic field. Further coupling is introduced by 3D inhomogeneities in the ion density during the assimilation of injected pellets. This additional coupling modifies the Alfvén continuum and discrete eigenmode spectrum. The frequencies of Alfvén eigenmodes drop dramatically when a pellet is injected in JET. From these observations, information about the changes in the ion density caused by a pellet can be inferred. To use Alfvén eigenmodes for MHD spectroscopy of pellet injected plasmas, the 3D MHD codes Stellgap and AE3D were generalised to incorporate 3D density profiles. A model for the expansion of the ionised pellet plasmoid along a magnetic field line was derived from the fluid equations. Thereby, the time evolution of the Alfvén eigenfrequency is reproduced. By comparing the numerical frequency drop of a toroidal Alfvén eigenmode (TAE) to experimental observations, the initial ion density of a cigar-shaped ablation region of length 4cm is estimated to be n * = 6.8×10 22 m −3 at the TAE location (r/a ≈ 0.75). The frequency sweeping of an Alfvén eigenmode ends when the ion density homogenises poloidally. Modelling suggests that the time for poloidal homogenisation of the ion density at the TAE position is τ h = 18 ± 4 ms for inboard pellet injection, and τ h = 26 ± 2 ms for outboard pellet injection. By reproducing the frequency evolution of the elliptical Alfvén eigenmode (EAE), the initial ion density at the EAE location (r/a ≈ 0.9) can be estimated to be n * = 4.8 × 10 22 m −3. Poloidal homogenisation of the ion density takes 2.7 times longer at the EAE location than at the TAE location for both inboard and outboard pellet injection. MHD spectroscopy, Alfvén eigenmodes, pellet injection ‡ See the author list of "Overview of the JET preparation for Deuterium-Tritium Operation" by E.
A kinetic model is developed to determine the power deposition from energetic electrons into the neutral gas shield of an ablating high-Z pellet. For high-Z, the velocity distribution of the hot electrons is nearly isotropic, and we use this feature to develop solutions to the kinetic equation. In contrast to pre-existing models, we consider the effect of gyro-motion as well as elastic scattering of the hot electrons. Two limits are considered: when the gyro-frequency is much greater than the elastic collision frequency, the hot electrons diffuse longitudinally along the field lines as they slow down; but if the gyro-frequency is much less than the elastic collision frequency, the hot electrons diffuse radially. In both limits, it is possible to express the kinetic equation describing the hot electrons independently of the gas density profile, and therefore, the power deposition model is universal in this respect. The emphasis on elastic scattering yields an ablation rate which scales as Z−7/6 which is different than Z−2/3 shown in Sergeev et al (2006 Plasma Phys. Rep. 32 5). It is also shown that the sheath potential required to maintain ambipolarity in the cloud scales as Z−1/3. Fluid simulations yield ablation rates that scale with the four-thirds power of the pellet radius in agreement with [].
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