arXiv subjects

Roscoe B. White

Publications and source records attributed to Roscoe B. White.

5 recordsLinked to original sources

arXiv2026

Frequency-inference method for reduced modeling of energetic particle modes (EPM) utilizing resonant auto-optimization remnants of imperfect time-scale separation

Integrated codes simulating interactions between Alfvén waves and fast ions in tokamak plasmas use perturbative models for the relatively slow processes of instability growth, saturation, chirping and bursting, and transport. Faster processes by which an Alfvén mode's spatiotemporal structure forms are assumed to have been completed within the mode's oscillation period, $τ_0 \equiv 2π/ω_0$. This separation of time scales underlies the computational efficiency of perturbative models, where the Alfvén mode's time-dependence is reduced to that of a scalar signal $s(t) = A(t)\sin(-ω_0 t - ϕ(t))$ with variable amplitude $A(t)$ and phase $ϕ(t)$. For this, accurate input data in the form of a mode's spatial structure $δΦ({\mathbf x})$, damping rate $γ_{\rm d}$, and initial frequency $ω_0$ are required. For modes residing in dense or continuous spectra, $δΦ$ and $γ_{\rm d}$ could be estimated from the form of the continua and fast ion orbits, but it is difficult to guess the seed frequency $ω_0$. Here, we report results of numerical experiments showing that it is possible to find $ω_0$ using a prompt frequency shift that occurs during the first few $100$ time steps of a simulation. Restarts with the shifted frequency iteratively converge to a value of $ω_0$ that seems to maximize the resonant drive, suggesting an auto-optimization process. The need for iteration is attributed to the fact that the terms required for rapid frequency adjustments were truncated when deriving the perturbative model. Meanwhile, the fact that partial auto-optimization is possible at all is attributed to the fact that series truncation alone (without filter) does not strictly enforce slowness. Remnants of and cross-talk with faster dynamics still occur in numerical implementations. This entails potential for both uncertainty and utility.

physics.plasm-ph↗

arXiv2025

Energetic-particle orbits near rational flux surfaces in stellarators: I. Passing particles

Recent simulations have shown that, even when the magnetic field of a stellarator possesses nested toroidal flux surfaces, the orbits of passing energetic particles can exhibit islands. These 'drift islands' arise near rational flux surfaces, where they are likely to enhance alpha-particle transport -- flattening the alpha density profile locally -- unless they can be avoided by suitable design of the stellarator magnetic field. To investigate how this might be achieved, we derive an equation for the drift-island shape in a general stellarator. This result follows from the solution to a more fundamental problem: that of calculating the orbits of passing particles near a rational flux surface. We show that these orbits are determined by conservation of an adiabatic invariant associated with the closed rational-surface field lines. We use this 'transit adiabatic invariant' to prove that there are no drift islands, for all passing particles, if and only if the magnetic field satisfies a weaker version of the Cary-Shasharina condition for omnigeneity; we call such magnetic fields 'cyclometric'. The drift-island width scales as $\sim (ρ_\starδ/s)^{1/2} a$ ($ρ_\star$ is the normalized gyroradius, $δ$ is the deviation from cyclometry, $s$ is the magnetic shear, and $a$ is the minor radius), so large drift islands could arise in low-shear stellarators that are insufficiently cyclometric. To ensure accurate results for very energetic particles, we compute higher-order corrections to the transit invariant. Our calculations agree extremely well with ASCOT5 guiding-centre and full-orbit simulations of alpha particles in reactor-scale equilibria, even at $3.5\text{MeV}$. Finally, we show how our results can also be derived using Hamiltonian perturbation theory, which provides a systematic framework for calculating passing-particle orbits on both rational and irrational surfaces.

physics.plasm-ph↗

arXiv2022

Testing the conservative character of particle simulations: I. Canonical and noncanonical guiding center model in Boozer coordinates

The guiding center (GC) Lagrangian in Boozer coordinates for toroidally confined plasmas can be cast into canonical form by eliminating a term containing the covariant component $B_{Ψ_{\rm P}}$ of the magnetic field vector with respect to the poloidal flux function $Ψ_{\rm P}$. Considering fast ions in the presence of a shear Alfvén wave field with fixed amplitude, fixed frequency and a single toroidal mode number $n$, we show that simulations using the code ORBIT with and without $B_{Ψ_{\rm P}}$ yield practically the same resonant and nonresonant GC orbits. The numerical results are consistent with theoretical analyses (presented in the Appendix), which show that the unabridged GC Lagrangian with $B_{Ψ_{\rm P}}$ retained yields equations of motion that possess two key properties of Hamiltonian flows: (i) phase space conservation, and (ii) energy conservation. As counter-examples, we also show cases where energy conservation (ii) or both conservation laws (i) & (ii) are broken by omitting certain small terms. When testing the conservative character of the simulation code, it is found to be beneficial to apply perturbations that do not resemble normal (eigen)modes of the plasma. The deviations are enhanced and, thus, more easily spotted when one inspects wave-particle interactions using nonnormal modes.

physics.plasm-ph↗

arXiv2021

On the effect of beating during nonlinear frequency chirping

Spectral analyses of energetic particle (EP) driven bursts of MHD fluctuations in magnetically confined plasmas often exhibit multiple simultaneous chirps. While the superposition of oscillations at multiple frequencies necessarily causes beating in the signal acquired by a localized external probe, self-consistent hybrid simulations of chirping EP modes in a JT-60U tokamak plasma have demonstrated the possibility of global beating, where the electromagnetic field vanishes globally between beats and reappears with opposite phase. This implies that there can be a single field mode that oscillates at multiple frequencies simultaneously when resonantly driven by multiple density waves in EP phase space. Conversely, this means that the EP density waves are mutually coupled and interfere with each other via the jointly driven field, a mechanism ignored in some theories. In this treatise, we study the role of field pulsations in general and beating in particular using the Hamiltonian guiding center orbit-following code ORBIT with a reduced wave-particle interaction model in realistic geometry. Through amplitude pulsations and phase jumps, beating is found to drive the evolution of EP phase space structures. Observations: (1) Beating causes density wave fronts to advance radially in pulses. The resulting chirps become staircase-like. (2) The beats facilitate convective transfer of material between neighboring layers of phase space density waves. On the one hand, this may delay detachment of solitary vortices. On the other hand, it facilitates the accumulation of hole and clump fragments into larger structures. (3) Long-range chirping occurs when massive holes or clumps detach and drift away from the turbulent belt around the seed resonance. The detached vortices can remain robust and, on average, maintain their concentric nested layers while being perturbed by the field's continued beating.

physics.plasm-ph↗

arXiv2005

Effect of Noise on the Standard Mapping

The effect of a small amount of noise on the standard mapping is considered. Whenever the standard mapping possesses accelerator modes (where the action increases approximately linearly with time), the diffusion coefficient contains a term proportional to the reciprocal of the variance of the noise term. At large values of the stochasticity parameter, the accelerator modes exhibit a universal behavior. As a result the dependence of the diffusion coefficient on the stochasticity parameter also shows some universal behavior.

nlin.CD↗