Hamiltonian Theory of Adiabatic Motion of Relativistic Charged Particles

High Order Explicit Lorentz Invariant Volume-preserving Algorithms for Relativistic Dynamics of Charged Particles

Lorentz invariant structure-preserving algorithms possess reference-independent secular stability, which is vital for simulating relativistic multi-scale dynamical processes. The splitting method has been widely used to construct structure-preserving algorithms, but without exquisite considerations, it can easily break the Lorentz invariance of continuous systems. In this paper, we introduce a Lorentz invariant splitting technique to construct high order explicit Lorentz invariant volume-preserving algorithms (LIVPAs) for simulating charged particle dynamics. Using this method, long-term stabl…

Explicit High-Order Gauge-Independent Symplectic Algorithms for Relativistic Charged Particle Dynamics

Symplectic schemes are powerful methods for numerically integrating Hamiltonian systems, and their long-term accuracy and fidelity have been proved both theoretically and numerically. However direct applications of standard symplectic schemes to relativistic charged particle dynamics result in implicit and electromagnetic gauge-dependent algorithms. In the present study, we develop explicit high-order gauge-independent noncanonical symplectic algorithms for relativistic charged particle dynamics using a Hamiltonian splitting method in the 8D phase space. It also shown that the developed algori…

On the Mechanism of the Volume Reflection of Relativistic Particles

The mechanisms of the volume reflection of positively and negatively charged relativistic particles in a bent crystal have been analyzed. It has been shown that the empty core effect is significant for the negatively charged particles. The average reflection angle of the negatively charged particles has been determined and the conditions for the observation of the reflection and refraction are discussed.

Collisional Energy Loss of Fast Charged Particles in Relativistic Plasmas

Following an argument by Kirzhnits we rederive an exact expression for the energy loss of a fast charged particle in a relativistic plasma using the quantum field theoretical language. We compare this result to perturbative calculations of the collisional energy loss of an energetic electron or muon in an electron-positron plasma and of an energetic parton in the quark-gluon plasma.

相对论性带电粒子动力学的蛙跳方法

Leapfrog methods for relativistic charged-particle dynamics

针对电磁场中相对论性带电粒子运动方程，提出基于四维表述的蛙跳积分器及其保能量、变分/辛变体，并分析其保结构性质及非相对论极限。

Density shocks in the relativistic expansion of highly charged one component plasmas

In a previous paper we showed that dynamical density shocks occur in the non-relativistic expansion of dense single component plasmas relevant to ultrafast electron microscopy; and we showed that fluid models capture these effects accurately. We show that the non-relativistic decoupling of the relative and center of mass motions ceases to apply and this coupling leads to novel behavior in the relativistic dynamics under planar, cylindrical, and spherical symmetries. In cases where the relative motion of the bunch is relativistic, we show that a dynamical shock emerges even in the case of a uni…

Self modulated dynamics of a relativistic charged particle beam in plasma wake field excitation

Self modulated dynamics of a relativistic charged particle beam is reviewed within the context of the theory of plasma wake field excitation. The self-consistent description of the beam dynamics is provided by coupling the Vlasov equation with a Poisson-type equation relating the plasma wake potential to the beam density. An analysis of the beam envelope self-modulation is then carried out and the criteria for the occurrence of the instability are discussed thereby.

High order volume-preserving algorithms for relativistic charged particles in general electromagnetic fields

We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general construction of volume-preserving methods that can be applied to systems with time-dependent electromagnetic fields. The newly derived methods provide numerical solutions with good accuracy and conservative properties over long time of simulation. Furthermore, because of the use of processing technique the high order methods are explicit, and cost less than the method…