NChargedBodyTreecode.jl

by Yi-Kai Kan ([email protected])

This package provides treecode algorithms for calculating the relativistic space-charge field. The treeocodes are implemented based on the tensor-product interpolation with Lagragian polynomials.

Installation

The package can be installed using Julia's REPL

julia> import Pkg
julia> Pkg.add(url="https://github.com/ykkan/NChargedBodyTreecode.git")

or with Pkg mode (hitting ] in the command prompt)

pkg> add https://github.com/ykkan/NChargedBodyTreecode.git

Usage

Creating a Charged Particle Beam

A charged particle beam can be created by providing an array of particle position and an array of particle momentum.

using NChargedBodyTreecode

# number of particles
const N = 1000    

# create position and momentum distribution of N particles
positions = rand(3, N)
momenta = zeros(3, N)

# create a particle beam in which each particle's charge and mass are -1 and 1 
beam = Particles(; pos=positions, mom=momenta, charge=-1.0, mass=1.0) 

Space-Charge Field Calculation

The space-charge field of a particle beam can be evaluated using updateParticlesField! with different algorithms:

• BruteForce: brute-forece method
• TreecodeStretch: treecode with stretched admissibility condition
• TreecodeAvgRestFrame: treecode using average rest-frame technique
• TreecodeUniform: treecode with conventional admissibility condition

using NChargedBodyTreecode
# update particle field by brute-force method (lambda is a characteristic length for the normalization of length quantity)

updateParticlesField!(beam0, BruteForce(); lambda=1.0)

# update particle field by different treecode methods with the following parameters: 
#   n: degree of interpolation
#   N0: maximum number of particles in the leaf cluster
#   eta: admissibility parameter 
#   lambda: a characteristic length for the normalization of length quantity
####
const n = 2 
const N0 = 20  
const eta = 0.5
updateParticlesField!(beam1, TreecodeStretch(eta=eta, N0=N0, n=n); lambda=1.0)
updateParticlesField!(beam2, TreecodeAvgRestFrame(eta=eta, N0=N0, n=n); lambda=1.0)
updateParticlesField!(beam3, TreecodeUniform(eta=eta, N0=N0, n=n); lambda=1.0)

# relative errors of different treecodes (comparing to brute-force)
error1 = relerror(beam1, beam0) 
error2 = relerror(beam2, beam0)
error3 = relerror(beam3, beam0)

The space-charge field (both E- and B-field) of beam is stored in beam.efields and beam.bfields (both have a type Vector{SVector{3,T}}, see StaticArrays for more details).

After the update of space-charge field of beam, the space-charge field on i-th particle can be accessed by, for example

efield = beam.efields[i]
bfield = beam.bfields[i]

More details can found in the demo file from examples/

Reference

Y.-K. Kan, F. X. Kärtner, S. Le Borne, and J.-P. M. Zemke, Relativistic Space-Charge Field Calculation by Interpolation-Based Treecode, Comput. Phys. Commun. 286 (2023), 108668.