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/* Copyright 2019 David Grote, Maxence Thevenet, Remi Lehe
* Weiqun Zhang
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#ifndef WARPX_PARTICLES_PUSHER_UPDATEMOMENTUM_VAY_H_
#define WARPX_PARTICLES_PUSHER_UPDATEMOMENTUM_VAY_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 UpdateMomentumVay(
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::Real q, const amrex::Real m, const amrex::Real dt )
{
using namespace amrex::literals;
// Constants
const amrex::Real econst = q*dt/m;
const amrex::Real bconst = 0.5_rt*q*dt/m;
constexpr amrex::Real invclight = 1._rt/PhysConst::c;
constexpr amrex::Real invclightsq = 1._rt/(PhysConst::c*PhysConst::c);
// Compute initial gamma
const amrex::Real inv_gamma = 1._rt/std::sqrt(1._rt + (ux*ux + uy*uy + uz*uz)*invclightsq);
// Get tau
const amrex::Real taux = bconst*Bx;
const amrex::Real tauy = bconst*By;
const amrex::Real tauz = bconst*Bz;
const amrex::Real tausq = taux*taux+tauy*tauy+tauz*tauz;
// Get U', gamma'^2
const amrex::Real uxpr = ux + econst*Ex + (uy*tauz-uz*tauy)*inv_gamma;
const amrex::Real uypr = uy + econst*Ey + (uz*taux-ux*tauz)*inv_gamma;
const amrex::Real uzpr = uz + econst*Ez + (ux*tauy-uy*taux)*inv_gamma;
const amrex::Real gprsq = (1._rt + (uxpr*uxpr + uypr*uypr + uzpr*uzpr)*invclightsq);
// Get u*
const amrex::Real ust = (uxpr*taux + uypr*tauy + uzpr*tauz)*invclight;
// Get new gamma
const amrex::Real sigma = gprsq-tausq;
const amrex::Real gisq = 2._rt/(sigma + std::sqrt(sigma*sigma + 4._rt*(tausq + ust*ust)) );
// Get t, s
const amrex::Real bg = bconst*std::sqrt(gisq);
const amrex::Real tx = bg*Bx;
const amrex::Real ty = bg*By;
const amrex::Real tz = bg*Bz;
const amrex::Real s = 1._rt/(1._rt+tausq*gisq);
// Get t.u'
const amrex::Real tu = tx*uxpr + ty*uypr + tz*uzpr;
// Get new U
ux = s*(uxpr+tx*tu+uypr*tz-uzpr*ty);
uy = s*(uypr+ty*tu+uzpr*tx-uxpr*tz);
uz = s*(uzpr+tz*tu+uxpr*ty-uypr*tx);
}
#endif // WARPX_PARTICLES_PUSHER_UPDATEMOMENTUM_VAY_H_
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