Compressional Alfvén eigenmodes in rotating spherical tokamak plasmas

Abstract

Abstract. Spherical tokamaks often have a considerable toroidal plasma rotation of several tens of kHz. Compressional Alfvén eigenmodes (CAEs) in such devices therefore experience a frequency shift, which if the plasma were rotating as a rigid body, would be a simple Doppler shift. However, since the rotation frequency depends on minor radius, the eigenmodes are affected in a more complicated way. The eigenmode solver CAE3B [Smith et al. Plasma Phys. Control. Fusion 51, 075001 (2009)] has been extended to account for toroidal plasma rotation. The results show that the eigenfrequency shift due to rotation can be approximated by a rigid body rotation with a frequency computed from a spatial average of the real rotation profile weighted with the eigenmode amplitude. To investigate the effect of extending the computational domain to the vessel wall, a simplified eigenmode equation, yet retaining plasma rotation, is solved by a modified version of the CAE code used in [Fredrickson et al. Phys. Plasmas 20, 042112 (2013)]. In summary, both solving the full eigenmode equation, as in the CAE3B code, and placing the boundary at the vessel wall, as in the CAE code, significantly influences the calculated eigenfrequencies.

Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. II. Interaction via Landau resonance

“…Hence, one of these lower bounds will always be redundant. An upper bound on k /k ⊥ can be derived heuristically, considering that the CAEs are trapped in a local effective potential well 8,9,12,14,15 of characteristic width ∆R ≈ R 0 /2. To satisfy this constraint, an integer number of half wavelengths must fit within the potential well, such that k R,min = π/∆R.…”

“…They are polarized with finite δB • k ⊥ and δB . In tokamak geometry, the mode becomes confined within an effective potential well [7][8][9][10][11][12][13][14][15] with discrete frequencies resulting from the boundary conditions. GAEs are a class of weakly damped shear MHD waves that can exist just below or above 16 an extremum in the continuum of solutions for shear Alfvén waves satisfying ω = k (r) v A (r).…”

Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. I. Interaction via ordinary and anomalous cyclotron resonances

“…In a cold, uniform plasma, they have dispersion ω = kv A and ω = k v A , where v A = B/ √ µ 0 n i m i is the Alfvén speed. In realistic toroidal geometries with spatial inhomogeneities, the CAE will become localized in the magnetic well in a standing wave configuration [18][19][20][21][22] with the spectrum of eigenmodes depending on the details of the magnetic geometry. [23][24][25][26] Likewise, the shear Alfvén dispersion becomes spatially dependent in a non-uniform plasma, and modes within this continuum of solutions become strongly damped due to phase mixing.…”

Hybrid simulations of sub-cyclotron compressional and global Alfvén Eigenmode stability in spherical tokamaks

“…Regardless of the poloidal mode numbers ascribed to them, the CAE mode structures from the HYM simulations presented here qualitatively match the CAE eigenmodes found by the CAE3B eigensolver for a separate NSTX discharge 130335. 38 The similarity between the HYM and CAE3B mode structures provides further ev- idence that the instabilities seen in HYM and heuristically identified as CAE due to large δB in the core are indeed CAE solutions. Comparison against the CAE dispersion relation further supports the classification of these modes.…”