Time step of ux/uy/uz and Ex/Ey/Ez(Bx/By/Bz).

[zhazhajust]

I want to add a new pusher, but i don't know the time align of the physic variable.

For example, is this boris method use the n - 1/2 step ux, uy, uz and n step Ex, Ey, Ez and Bx, By, Bz to get n + 1/2 step ux, uy, uz?
Where is the time step of postion (x, y, z) before and after PushXP() function?
And how to make the Bx, By Bz to align with n step rather than n + 1/2 step in FDTD method?

/* 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_BORIS_H_
#define WARPX_PARTICLES_PUSHER_UPDATEMOMENTUM_BORIS_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 UpdateMomentumBoris(
    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;

    const amrex::ParticleReal econst = 0.5_prt*q*dt/m;

    // First half-push for E
    ux += econst*Ex;
    uy += econst*Ey;
    uz += econst*Ez;
    // Compute temporary gamma factor
    constexpr amrex::ParticleReal inv_c2 = 1._prt/(PhysConst::c*PhysConst::c);
    const amrex::ParticleReal inv_gamma = 1._prt/std::sqrt(1._prt + (ux*ux + uy*uy + uz*uz)*inv_c2);
    // Magnetic rotation
    // - Compute temporary variables
    const amrex::ParticleReal tx = econst*inv_gamma*Bx;
    const amrex::ParticleReal ty = econst*inv_gamma*By;
    const amrex::ParticleReal tz = econst*inv_gamma*Bz;
    const amrex::ParticleReal tsqi = 2._prt/(1._prt + tx*tx + ty*ty + tz*tz);
    const amrex::ParticleReal sx = tx*tsqi;
    const amrex::ParticleReal sy = ty*tsqi;
    const amrex::ParticleReal sz = tz*tsqi;
    const amrex::ParticleReal ux_p = ux + uy*tz - uz*ty;
    const amrex::ParticleReal uy_p = uy + uz*tx - ux*tz;
    const amrex::ParticleReal uz_p = uz + ux*ty - uy*tx;
    // - Update momentum
    ux += uy_p*sz - uz_p*sy;
    uy += uz_p*sx - ux_p*sz;
    uz += ux_p*sy - uy_p*sx;
    // Second half-push for E
    ux += econst*Ex;
    uy += econst*Ey;
    uz += econst*Ez;
}

#endif // WARPX_PARTICLES_PUSHER_UPDATEMOMENTUM_BORIS_H_

Is there anyway to get the ux, uy, uz at n - 1/2 and n + 1/2 timestep and x/y/z/Ex/Ey/Ez/Bx/By/Bz at n timestep.

[RemiLehe]

You are correct: in the WarpX code, the boris method uses the n - 1/2 step ux, uy, uz and the n step Ex, Ey, Ez and Bx, By, Bz to get n + 1/2 step ux, uy, uz. (In particular, in WarpX, even when using FDTD, the B field is known at the n step - because we perform to half-step push of B)

The positions x, y, z are also known at the n step before calling PushXP. They are known at the n+1 step after calling PushXP.