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/* Copyright 2019 Yinjian Zhao
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#ifndef WARPX_PARTICLES_PUSHER_UPDATEMOMENTUM_HIGUERACARY_H_
#define WARPX_PARTICLES_PUSHER_UPDATEMOMENTUM_HIGUERACARY_H_
#include "Utils/WarpXConst.H"
#include <AMReX_FArrayBox.H>
#include <AMReX_REAL.H>
/**
* \brief Push the particle's positions over one timestep,
* given the value of its momenta `ux`, `uy`, `uz`
*/
AMREX_GPU_HOST_DEVICE AMREX_INLINE
void UpdateMomentumHigueraCary(
amrex::ParticleReal& ux, amrex::ParticleReal& uy, amrex::ParticleReal& uz,
const amrex::ParticleReal Ex, const amrex::ParticleReal Ey, const amrex::ParticleReal Ez,
const amrex::ParticleReal Bx, const amrex::ParticleReal By, const amrex::ParticleReal Bz,
const amrex::ParticleReal q, const amrex::ParticleReal m, const amrex::Real dt )
{
using namespace amrex::literals;
// Constants
const amrex::ParticleReal qmt = 0.5_prt*q*dt/m;
constexpr amrex::ParticleReal invclight = 1._prt/PhysConst::c;
constexpr amrex::ParticleReal invclightsq = 1._prt/(PhysConst::c*PhysConst::c);
// Compute u_minus
const amrex::ParticleReal umx = ux + qmt*Ex;
const amrex::ParticleReal umy = uy + qmt*Ey;
const amrex::ParticleReal umz = uz + qmt*Ez;
// Compute gamma squared of u_minus
amrex::ParticleReal gamma = 1._prt + (umx*umx + umy*umy + umz*umz)*invclightsq;
// Compute beta and betam squared
const amrex::ParticleReal betax = qmt*Bx;
const amrex::ParticleReal betay = qmt*By;
const amrex::ParticleReal betaz = qmt*Bz;
const amrex::ParticleReal betam = betax*betax + betay*betay + betaz*betaz;
// Compute sigma
const amrex::ParticleReal sigma = gamma - betam;
// Get u*
const amrex::ParticleReal ust = (umx*betax + umy*betay + umz*betaz)*invclight;
// Get new gamma inversed
gamma = 1._prt/std::sqrt(0.5_prt*(sigma + std::sqrt(sigma*sigma + 4._prt*(betam + ust*ust)) ));
// Compute t
const amrex::ParticleReal tx = gamma*betax;
const amrex::ParticleReal ty = gamma*betay;
const amrex::ParticleReal tz = gamma*betaz;
// Compute s
const amrex::ParticleReal s = 1._prt/(1._prt+(tx*tx + ty*ty + tz*tz));
// Compute um dot t
const amrex::ParticleReal umt = umx*tx + umy*ty + umz*tz;
// Compute u_plus
const amrex::ParticleReal upx = s*( umx + umt*tx + umy*tz - umz*ty );
const amrex::ParticleReal upy = s*( umy + umt*ty + umz*tx - umx*tz );
const amrex::ParticleReal upz = s*( umz + umt*tz + umx*ty - umy*tx );
// Get new u
ux = upx + qmt*Ex + upy*tz - upz*ty;
uy = upy + qmt*Ey + upz*tx - upx*tz;
uz = upz + qmt*Ez + upx*ty - upy*tx;
}
#endif // WARPX_PARTICLES_PUSHER_UPDATEMOMENTUM_HIGUERACARY_H_
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