Testing the conservative character of particle simulations: II. Spurious heating of guiding centers and full orbits subject to fluctuations expressed in terms of E and B

Abstract

For an axisymmetric tokamak plasma, Hamiltonian theory predicts that the orbits of charged particles must stay on invariant tori of conserved energy in the moving frame of reference of a wave that propagates along the torus with fixed angular phase velocity, amplitude, and shape. The mode structure in the poloidal plane is arbitrary if the fluctuations are expressed in terms of potentials [Formula: see text] and [Formula: see text], which satisfy Faraday's law and the solenoidal condition by definition. Consequently, smoothing operations (such as gyroaveraging and noise suppression) do not violate the conservative laws. However, this is not guaranteed for models expressed in terms of the physical fields [Formula: see text] and [Formula: see text]. Here, we demonstrate that manipulations of [Formula: see text] and [Formula: see text] in the poloidal ( R, z) plane can cause spurious heating that is independent of time steps or numerical methods, but can be sensitive to geometry. In particular, we show that secular acceleration is enhanced when one imposes nonnormal modes that possess strong up–down asymmetry instead of the usual in–out asymmetry of normal toroidal (eigen)modes. We compare full gyro-orbit and guiding center models and find similar behavior. We also examine the effect of ad hoc N-point gyroaveraging in a guiding center model, as is done in some simulation codes. If one uses Faraday's law to (re)compute [Formula: see text] after gyroaveraging [Formula: see text], the guiding center motion remains conservative. Otherwise, spurious heating should be expected and monitored, but it may be tolerable when normal modes dominate.