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A description of a bounce-averaged Fokker–Planck quasilinear model for the kinetic description of tokamak plasmas is presented. The nonlinear collision and quasilinear resonant diffusion operators are represented in a form conducive to numerical solution with specific attention to the treatment of the boundary layer separating trapped and passing orbit regions of velocity space. The numerical techniques employed are detailed insofar as they constitute significant departure from those used in the conventional uniform magnetic field case. Examples are given to illustrate the combined effects of collisional and resonant diffusion.

A new relativistic, bounce-averaged Fokker-Planck-quasilinear code shows that for experimentally relevant rf power /7 r f(W/cm 3 )/[« e (10 13 cm _3 )] 2^0 .5, electron-cyclotron current-drive efficiency (and absorptivity) is power dependent; at given plasma radius the current-drive efficiency increases above linear values for absorption of the rf on the low-field side of the cyclotron resonance layer, but decreases and even passes through zero for absorption on the high-field side. Thus, electron-cyclotron current drive by high-field launch will generally not be suitable.PACS numbers: 52.50.Gj, 52.55.Fa A tokamak reactor is a much more attractive concept as a fusion power device if it is run at steady state. This can be accomplished with an efficient source of toroidal current, other than inherently pulsed inductive drive. Electron-cyclotron (EC) waves are particularly suitable for this purpose because they readily penetrate into high-density, high-temperature tokamak plasma, and because the damping process is easily controlled in configuration and velocity space. A limitation is that the frequency of the wave source must be sufficiently high to avoid plasma cutoff. At elevated density this presents technological difficulties. However, the required frequency is reduced for waves absorbed on the inboard, high-field side of the resonance layer, compared to waves absorbed on the outboard, low-field side. Thus, in Ref.1, high-field absorption has been proposed for the heating of the conceptual compact ignition tokamak (CIT) at elevated density (n e -10 15 cm -3 ). Moreover, past work 2 has shown that EC current-drive efficiency with absorption outside the cyclotron layer is degraded in practical situations at temperatures greater than 20 keV by overlap of neighboring cyclotron interactions, which drives current in opposite directions. Unfortunately, as evidenced by the results presented here, the inside launch configuration is not suitable for high-power rf current generation. In this Letter we study the EC current drive as a function of applied power, for cases of absorption on the high-or the low-field side of the resonance layer. We find that current drive by absorption on the highfield side is problematical because of a reduction of current-drive efficiency as a function of increasing applied power, but for absorption on the low-field side the efficiency increases at high power.The relationship between the region of velocity space affected by the waves and the spatial location of the absorption elucidates the dominant physical effects. At a given spatial point in the tokamak, the incoming wave resonates with electron-cyclotron motion satisfying v\\ = (co -l(o ce /y)/k\\, where v\\ is the electron velocity parallel to the magnetic field, co and k\\ are wave frequency and parallel wave number, / is the cyclotron har-monic, co ce is the cyclotron frequency which varies inversely with major radius R, and y is the relativistic mass factor. This resonance condition corresponds to an ellipse in (v\\,v±) space (v=p/m e...

Rapid growth and perivascular invasion are hallmarks of glioblastoma (GBM) that have been attributed to the presence of cancer stem-like cells (CSCs) and their association with the perivascular niche. However, the mechanisms by which the perivascular niche regulates GBM invasion and CSCs remain poorly understood due in part to a lack of relevant model systems. To simulate perivascular niche conditions and analyze consequential changes of GBM growth and invasion, patient-derived GBM spheroids were co-cultured with brain endothelial cells (ECs) in microfabricated collagen gels. Integrating these systems with 3D imaging and biochemical assays revealed that ECs increase GBM invasiveness and growth through interleukin-8 (IL-8)-mediated enrichment of CSCs. Blockade of IL-8 inhibited these effects in GBM-EC co-cultures, while IL-8 supplementation increased CSC-mediated growth and invasion in GBM-monocultures. Experiments in mice confirmed that ECs and IL-8 stimulate intracranial tumor growth and invasion in vivo . Collectively, perivascular niche conditions promote GBM growth and invasion by increasing CSC frequency, and IL-8 may be explored clinically to inhibit these interactions.

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