Preliminary Simulations of FLR Effects on RFP Tearing Modes

Kim, Charlson C.

doi:10.1007/s10894-007-9117-y

Cited by 4 publications

(10 citation statements)

References 12 publications

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“…For example, in actual hybrid simulations of the non-Hamiltonian PCS in fusion devices, toroidal symmetry is involved and the use of special equilibrium profiles becomes necessary [29]. Another example arises in reversed field pinch plasmas, in which finite Larmor radius effects allow for equilibria of the type [11]). On the other hand, the aim here is not to enter into detailed features of particular fusion devices, but to provide insight into model differences.…”

Section: A Equations Of Motionmentioning

confidence: 99%

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Hybrid Vlasov-MHD models: Hamiltonian vs. non-Hamiltonian

Tronci

Tassi

Camporeale

et al. 2014

Plasma Phys. Control. Fusion

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This paper investigates hybrid kinetic-MHD models, where a hot plasma (governed by a kinetic theory) interacts with a fluid bulk (governed by MHD). Different nonlinear coupling schemes are reviewed, including the pressure-coupling scheme (PCS) used in modern hybrid simulations. This latter scheme suffers from being non-Hamiltonian and to not exactly conserve total energy. Upon adopting the Vlasov description for the hot component, the non-Hamiltonian PCS and a Hamiltonian variant are compared. Special emphasis is given to the linear stability of Alfvén waves, for which it is shown that a spurious instability appears at high frequency in the non-Hamiltonian version. This instability is removed in the Hamiltonian version.

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Section: A Equations Of Motionmentioning

confidence: 99%

“…In plasma fusion, the first two options are used most often, while the full Vlasov description is needed for e.g. reverse field pinch plasmas [11]. The full Vlasov description solves for effects at all scales and thus is less convenient when the hot particle gyromotion can be averaged out, in favor of drift-kinetic and gyro-kinetic models.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Vlasov-MHD models: Hamiltonian vs. non-Hamiltonian

Tronci

Tassi

Camporeale

et al. 2014

Plasma Phys. Control. Fusion

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“…Other than energy conservation, the PCS model ( 55)-( 57) also enjoys cross-helicity conservation, as it emerges from direct application of equation (30). To see this, we recall the definition K gc = m h ´µ(b • v) f d 3 v and write (30) more explicitly as…”

Section: Discussion and Conservation Lawsmentioning

confidence: 99%

“…1992, 1999) – but also that the physical consistency of available codes may be undermined in the fully nonlinear regime. Indeed, while considering the PCS with Vlasov kinetics (Kim 2008), Tronci et al. (2014) showed that spurious high-frequency instabilities are triggered by unphysical energy sources, thereby affecting the physical reliability of the continuum model underlying the simulation code.…”

Section: Nonlinear Hybrid Models For Energetic Particlesmentioning

confidence: 99%

“…This scenario shows not only that the CCS and the PCS are far from being equivalent -thereby disproving a commonly held belief (Park et al 1992(Park et al , 1999 -but also that the physical consistency of available codes may be undermined in the fully nonlinear regime. Indeed, while considering the PCS with Vlasov kinetics (Kim 2008), Tronci et al (2014) showed that spurious high-frequency instabilities are triggered by unphysical energy sources, thereby affecting the physical reliability of the continuum model underlying the simulation code. A potential criticism of this point is that high-frequency instabilities are irrelevant in fusion devices where the processes of interest take place at frequencies well below the cyclotron frequency of the energetic particles.…”

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confidence: 99%

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A low-frequency variational model for energetic particle effects in the pressure-coupling scheme

Burby

Tronci

2018

J. Plasma Phys.

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Energetic particle effects in magnetic confinement fusion devices are commonly studied by hybrid kinetic-fluid simulation codes whose underlying continuum evolution equations often lack the correct energy balance. While two different kinetic-fluid coupling options are available (current-coupling and pressure-coupling), this paper applies the Euler-Poincaré variational approach to formulate a new conservative hybrid model in the pressure-coupling scheme. In our case the kinetics of the energetic particles are described by guiding center theory. The interplay between the Lagrangian fluid paths with phase space particle trajectories reflects an intricate variational structure which can be approached by letting the 4-dimensional guiding center trajectories evolve in the full 6-dimensional phase space. Then, the redundant perpendicular velocity is integrated out to recover a four-dimensional description. A second equivalent variational approach is also reported, which involves the use of phase space Lagrangians. Not only do these variational structures confer on the new model a correct energy balance, but also they produce a cross-helicity invariant which is lost in the other pressure-coupling schemes reported in the literature.

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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

Bierwage

Shinohara

2022

Physics of Plasmas

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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.

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Preliminary Simulations of FLR Effects on RFP Tearing Modes

Cited by 4 publications

References 12 publications

Hybrid Vlasov-MHD models: Hamiltonian vs. non-Hamiltonian

Hybrid Vlasov-MHD models: Hamiltonian vs. non-Hamiltonian

A low-frequency variational model for energetic particle effects in the pressure-coupling scheme

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

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