[Paper Review] Surfatron acceleration along magnetic field by oblique electrostatic waves

I. Y. Dodin, N. J. Fisch|arXiv (Cornell University)|Nov 20, 2011

Magnetic confinement fusion research3 citations

TL;DR

This paper demonstrates that nonrelativistic charged particles can be accelerated along a dc magnetic field via surfatron mechanism driven by obliquely propagating electrostatic waves, even when wave frequency exceeds gyrofrequency and phase velocity surpasses initial particle speed. The mechanism enables net parallel current generation in plasma through resonant particle trapping and momentum transfer, with key dynamics differing from electromagnetic wave cases due to electrostatic field structure.

ABSTRACT

Charged particles can be accelerated via surfatron mechanism along dc magnetic field by obliquely propagating electrostatic waves. In plasma, this mechanism can, in principle, produce an average parallel current, even when the wave frequency is much larger than the gyrofrequency and the wave phase velocity is much larger than particle initial velocities.

Motivation & Objective

• To investigate surfatron acceleration of nonrelativistic particles by obliquely propagating electrostatic waves in a weak dc magnetic field.
• To clarify how particle dynamics in electrostatic waves differ from those in electromagnetic waves under the surfatron mechanism.
• To determine whether the surfatron mechanism can produce a net average current along the magnetic field, even when wave frequency is much larger than gyrofrequency and phase velocity exceeds initial particle speeds.
• To provide a transparent, non-Hamiltonian analysis of the underlying particle trajectories and resonance conditions in momentum space.

Proposed method

• Formulation of particle equations of motion in a wave field with wavevector k and dc magnetic field B₀, using normalized units for clarity.
• Derivation of momentum evolution equations (Eqs. 3–8) and identification of conserved quantities, including a spherical momentum surface Sρ in phase space.
• Introduction of the resonance plane Ξ defined by p_z = u, where u = (cos α)⁻¹ is the longitudinal phase velocity, to classify particle trajectories.
• Classification of particle trajectories into Types A–D based on intersection with the resonance plane and dynamical behavior (trapped, diffusive, ballistic).
• Analysis of current drive via ensemble averaging over ring distributions L in momentum space, with focus on cases where L intersects the resonance plane Ξ.
• Numerical tracing of 2¹⁶ particle trajectories to compute ⟨Δp_z⟩ as a function of initial perpendicular momentum p_⊥₀, validating analytical predictions.

Experimental results

Research questions

• RQ1 Can surfatron acceleration along the magnetic field occur via obliquely propagating electrostatic waves, even when the wave frequency is much larger than the gyrofrequency?
• RQ2 How does the particle dynamics in electrostatic waves differ qualitatively from that in electromagnetic waves under the surfatron mechanism?
• RQ3 Under what conditions can the surfatron mechanism produce a net average current along the magnetic field in a plasma?
• RQ4 What role does the initial particle momentum distribution (e.g., ring distribution) play in determining the magnitude and sign of the net momentum transfer?
• RQ5 Can particles with initial parallel velocity much smaller than the wave phase velocity still gain significant parallel momentum through this mechanism?

Key findings

• The surfatron mechanism can produce a net average current along the magnetic field in plasma, even when the wave frequency is much larger than the gyrofrequency and the wave phase velocity exceeds the initial particle velocity.
• For initial ring distributions in momentum space with p_⊥₀ ≥ p̄_⊥(p_z₀), the average parallel momentum gain ⟨Δp_z⟩ is positive, with maximum current generated when the ring is tangent to the resonance plane Ξ.
• When p_⊥₀ < p̄_⊥(p_z₀), no current is generated as the ring does not intersect the resonance plane; for p_⊥₀ > p̄_⊥(p_z₀), current is reduced due to Type C trajectories spending time in p_z < p_z₀ regions.
• Particles initially with p_z₀ ≪ u still contribute to net current, distinguishing this mechanism from traditional Cherenkov-based current drive.
• The mechanism operates via quasiadiabatic, nonlinear dynamics in the regime Θ = Ω/ω_E ≪ 1, where ω_E is the effective wave frequency scale.
• Numerical simulations confirm that ⟨Δp_z⟩ ≥ 0 for all considered initial conditions, with the maximum value achieved at tangency between the ring L and the resonance plane Ξ.