TaperedPL.H

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/* Copyright 2022-2023 The Regents of the University of California, through Lawrence
 *           Berkeley National Laboratory (subject to receipt of any required
 *           approvals from the U.S. Dept. of Energy). All rights reserved.
 *
 * This file is part of ImpactX.
 *
 * Authors: Chad Mitchell, Axel Huebl
 * License: BSD-3-Clause-LBNL
 */
#ifndef IMPACTX_TAPEREDPL_H
#define IMPACTX_TAPEREDPL_H
 
#include "particles/ImpactXParticleContainer.H"
#include "mixin/alignment.H"
#include "mixin/beamoptic.H"
#include "mixin/thin.H"
#include "mixin/lineartransport.H"
#include "mixin/spintransport.H"
#include "mixin/named.H"
#include "mixin/nofinalize.H"
 
#include <AMReX_Extension.H>
#include <AMReX_Math.H>
#include <AMReX_REAL.H>
#include <AMReX_SIMD.H>
 
#include <cmath>
#include <stdexcept>
 
 
namespace impactx::elements
{
    struct TaperedPL
    : public mixin::Named,
      public mixin::BeamOptic<TaperedPL>,
      public mixin::LinearTransport<TaperedPL>,
      public mixin::Thin,
      public mixin::Alignment,
      public mixin::SpinTransport,
      public mixin::NoFinalize,
      // At least on Intel AVX512, there is a small overhead to vectorize this element
      // for pure phase-space pushes. But a win for spin-tracking. See:
      //   https://github.com/BLAST-ImpactX/impactx/pull/1002
      //   https://github.com/BLAST-ImpactX/impactx/pull/1499
      public amrex::simd::Vectorized<amrex::simd::native_simd_size_particlereal>
    {
        static constexpr auto type = "TaperedPL";
        using PType = ImpactXParticleContainer::ParticleType;

        TaperedPL (
            amrex::ParticleReal k,
            amrex::ParticleReal taper,
            int unit,
            amrex::ParticleReal dx = 0,
            amrex::ParticleReal dy = 0,
            amrex::ParticleReal rotation_degree = 0,
            std::optional<std::string> name = std::nullopt
        )
        : Named(std::move(name)),
          Alignment(dx, dy, rotation_degree),
          m_k(k), m_taper(taper), m_unit(unit)
        {
        }

        void reverse () { m_k = -m_k; }

        void compute_constants (RefPart const & refpart)
        {
            using namespace amrex::literals; // for _rt and _prt
 
            Alignment::compute_constants(refpart);
 
            // normalize focusing strength units to MAD-X convention if needed
            m_g = m_unit == 1 ? m_k / refpart.rigidity_Tm() : m_k;
 
            // additional constants needed for spin push
            m_beta = refpart.beta();
            m_ibeta = 1_prt / m_beta;
 
        }

        using BeamOptic::operator();

        template<typename T_Real=amrex::ParticleReal, typename T_IdCpu=uint64_t>
        AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
        void operator() (
            T_Real const & AMREX_RESTRICT x,
            T_Real const & AMREX_RESTRICT y,
            [[maybe_unused]] T_Real const & AMREX_RESTRICT t,
            T_Real & AMREX_RESTRICT px,
            T_Real & AMREX_RESTRICT py,
            [[maybe_unused]] T_Real const & AMREX_RESTRICT pt,
            [[maybe_unused]] T_IdCpu const & AMREX_RESTRICT idcpu,
            [[maybe_unused]] RefPart const & AMREX_RESTRICT refpart
        ) const
        {
            using namespace amrex::literals; // for _rt and _prt
            using amrex::Math::powi;
            using namespace std; // for cmath(float)
 
            // initialize output values
            // T_Real xout = x;
            // T_Real yout = y;
            // T_Real tout = t;
            T_Real pxout = px;
            T_Real pyout = py;
            // T_Real ptout = pt;
 
            // advance position and momentum
            // xout = x;
            pxout = px - m_g * ( x + m_taper*0.5_prt * (powi<2>(x) + powi<2>(y)) );
 
            // yout = y;
            pyout = py - m_g * ( y + m_taper * x * y );
 
            // tout = t;
            // ptout = pt;
 
            // assign updated values
            // x = xout;
            // y = yout;
            // t = tout;
            px = pxout;
            py = pyout;
            // pt = ptout;
        }

        using Thin::operator();
 

        template<typename T_Real=amrex::ParticleReal, typename T_IdCpu=uint64_t>
        AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
        void spin_and_phasespace_push (
            T_Real const & AMREX_RESTRICT x,
            T_Real const & AMREX_RESTRICT y,
            T_Real const & AMREX_RESTRICT t,
            T_Real & AMREX_RESTRICT px,
            T_Real & AMREX_RESTRICT py,
            T_Real const & AMREX_RESTRICT pt,
            T_Real & AMREX_RESTRICT sx,
            T_Real & AMREX_RESTRICT sy,
            T_Real & AMREX_RESTRICT sz,
            T_IdCpu const & AMREX_RESTRICT idcpu,
            RefPart const & AMREX_RESTRICT refpart
        ) const
        {
            using namespace amrex::literals; // for _rt and _prt
            using namespace std; // for cmath(float)
            using amrex::Math::powi;
 
            // The Thomas-BMT generator is evaluated at the transverse momentum
            // halfway through the kick, so that reversing the element (negating
            // the strength) produces the exact inverse rotation.
            T_Real const px_in = px;
            T_Real const py_in = py;
 
            // pure phase-space push (shared with the non-spin operator())
            (*this)(x, y, t, px, py, pt, idcpu, refpart);
 
            // transverse momenta at the kick midpoint
            T_Real const px_mid = 0.5_prt * (px_in + px);
            T_Real const py_mid = 0.5_prt * (py_in + py);
 
            // initialize the three components of the axis-angle vector
            T_Real lambdax = 0_prt;
            T_Real lambday = 0_prt;
            T_Real lambdaz = 0_prt;
 
            // compute multipole magnetic field normalized by q/mc:
            amrex::ParticleReal const gamma_ref = refpart.gamma();
            T_Real const Bx = -m_g * ( y + m_taper * x * y ) * gamma_ref * m_beta;
            T_Real const By = m_g * ( x + m_taper*0.5_prt * (powi<2>(x) + powi<2>(y)) ) * gamma_ref * m_beta;
            T_Real const Bz = 0_prt;
 
            // Electric field normalized by q/mc^2:
            T_Real const Ex = 0.0_prt;
            T_Real const Ey = 0.0_prt;
            T_Real const Ez = 0.0_prt;
 
            // Quantities required to evaluate the full Thomas-BMT precession
            // vector, at the midpoint transverse momentum.
            T_Real const Pnorm = sqrt(1_prt - 2_prt * pt * m_ibeta + pt*pt);
            T_Real const iPnorm = 1_prt/Pnorm;
            T_Real const Ps = sqrt(Pnorm*Pnorm - px_mid*px_mid - py_mid*py_mid);
            T_Real const gamma = gamma_ref * (1_prt - pt*m_beta);
            T_Real const ux = px_mid * iPnorm;
            T_Real const uy = py_mid * iPnorm;
            T_Real const uz = Ps * iPnorm;
 
            // Zero curvature in a quadrupole
            amrex::ParticleReal const h = 0.0_prt;
 
            // Evaluation of the full Thomas-BMT precession vector.
            amrex::ParticleReal const gyro_anomaly = refpart.gyromagnetic_anomaly;
            tbmt_precession_vector(x, ux, uy, uz, gamma, h, gyro_anomaly, Bx, By, Bz, Ex, Ey, Ez, lambdax, lambday, lambdaz);
 
            // push the spin vector using the generator just determined
            rotate_spin(lambdax, lambday, lambdaz, sx, sy, sz);
 
        }
 

        using LinearTransport::operator();

        AMREX_GPU_HOST AMREX_FORCE_INLINE
        Map6x6
        transport_map (RefPart const & AMREX_RESTRICT refpart) const
        {
            using namespace amrex::literals; // for _rt and _prt
 
            // Normalize focusing strength to MAD-X convention if needed.
            amrex::ParticleReal const g = (m_unit == 1)
                ? m_k / refpart.rigidity_Tm()
                : m_k;
 
            // Linearized axisymmetric focusing kick; taper is quadratic
            // and therefore absent from the linear map.
            Map6x6 R = Map6x6::Identity();
            R(2,1) = -g;
            R(4,3) = -g;
 
            // apply the transverse rotation (roll) alignment error
            return rotate_aligned_map(R);
        }
 
        amrex::ParticleReal m_k; 
        amrex::ParticleReal m_taper; 
        int m_unit;  
 
      private:
        // constants that are independent of the individually tracked particle
        amrex::ParticleReal m_beta;           
        amrex::ParticleReal m_ibeta;          
        amrex::ParticleReal m_g;              
    };
 
} // namespace impactx
 
IMPACTX_PUSH_EXTERN_TEMPLATE(impactx::elements::TaperedPL)
 
#endif // IMPACTX_TAPEREDPL_H