Analytical solutions for global geodesic acoustic modes in the plasma of a tokamak with circular concentric magnetic surfaces are obtained. In the framework of ideal magnetohydrodynamics, an integral equation for eigenvalues (dispersion relation) taking into account toroidal coupling between electrostatic perturbations and electromagnetic perturbations with the poloidal mode number |m| = 2 is derived. In the absence of such coupling, the dispersion relation yields only the standard continuous spectrum. The existence of a global geodesic acoustic mode is analyzed for equilibria with both on-axis and off-axis maxima of the local geodesic acoustic frequency. The analytical results are compared with results of numerical calculations.
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机译：得到了具有圆形同心磁性表面的托卡马克等离子体中整体测地声模的解析解。在理想的磁流体动力学的框架中，特征值（色散关系）的积分方程考虑了静电扰动和电磁扰动之间的环形耦合，其极谱模数| m |。 = 2。在没有这种耦合的情况下，色散关系仅产生标准连续光谱。分析全局测地声模的存在与局部测地声频的轴上和轴外最大值的平衡。将分析结果与数值计算结果进行比较。
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