ImpactX
Kurth4D.H
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1 /* Copyright 2022-2023 The Regents of the University of California, through Lawrence
2  * Berkeley National Laboratory (subject to receipt of any required
3  * approvals from the U.S. Dept. of Energy). All rights reserved.
4  *
5  * This file is part of ImpactX.
6  *
7  * Authors: Chad Mitchell, Axel Huebl
8  * License: BSD-3-Clause-LBNL
9  */
10 #ifndef IMPACTX_DISTRIBUTION_KURTH4D
11 #define IMPACTX_DISTRIBUTION_KURTH4D
12 
13 #include <AMReX_Random.H>
14 #include <AMReX_REAL.H>
15 
16 #include <cmath>
17 
18 
19 namespace impactx
20 {
21 namespace distribution
22 {
23  struct Kurth4D
24  {
35  Kurth4D(amrex::ParticleReal const sigx, amrex::ParticleReal const sigy,
36  amrex::ParticleReal const sigt,amrex::ParticleReal const sigpx,
37  amrex::ParticleReal const sigpy,amrex::ParticleReal const sigpt,
38  amrex::ParticleReal const muxpx=0.0, amrex::ParticleReal const muypy=0.0,
39  amrex::ParticleReal const mutpt=0.0
40  )
41  : m_sigmaX(sigx),m_sigmaY(sigy),m_sigmaT(sigt),m_sigmaPx(sigpx),m_sigmaPy(sigpy),
42  m_sigmaPt(sigpt),m_muxpx(muxpx),m_muypy(muypy),m_mutpt(mutpt)
43  {
44  }
45 
58  amrex::ParticleReal & x,
59  amrex::ParticleReal & y,
60  amrex::ParticleReal & t,
61  amrex::ParticleReal & px,
62  amrex::ParticleReal & py,
63  amrex::ParticleReal & pt,
64  amrex::RandomEngine const& engine) const {
65 
66  using namespace amrex::literals;
67 
68  amrex::ParticleReal v,phi,r,u1,u2,ln1;
69  amrex::ParticleReal alpha,u,Lz,pmax,pr,pphi;
70  amrex::ParticleReal root,a1,a2;
71 
72  constexpr amrex::ParticleReal pi = 3.14159265358979_prt;
73 
74  // Sample and transform to define (x,y):
75  v = amrex::Random(engine);
76  phi = amrex::Random(engine);
77  phi = 2_prt*pi*phi;
78  r = sqrt(v);
79  x = r*cos(phi);
80  y = r*sin(phi);
81 
82  // Random samples used to define Lz:
83  u = amrex::Random(engine);
84  Lz = r*(2.0_prt*u-1.0_prt);
85 
86  // Random samples used to define pr:
87  alpha = amrex::Random(engine);
88  alpha = pi*alpha;
89  pmax = 1.0_prt - pow((Lz/r),2) - pow(r,2) + pow(Lz,2);
90  pmax = sqrt(pmax);
91  pr = pmax*cos(alpha);
92  pphi = Lz/r;
93 
94  // Transformations used to obtain (px,py):
95  px = pr*cos(phi)-pphi*sin(phi);
96  py = pr*sin(phi)+pphi*cos(phi);
97 
98  // Sample and transform to define (t,pt):
99  t = amrex::Random(engine);
100  t = 2.0_prt*(t-0.5_prt);
101  u1 = amrex::Random(engine);
102  u2 = amrex::Random(engine);
103  ln1 = sqrt(-2_prt*log(u1));
104  pt = ln1*cos(2_prt*pi*u2);
105 
106  // Scale to produce the identity covariance matrix:
107  amrex::ParticleReal c = sqrt(3.0_prt);
108  x = 2_prt*x;
109  y = 2_prt*y;
110  t = c*t;
111  px = 2_prt*px;
112  py = 2_prt*py;
113  // pt = pt;
114 
115  // Transform to produce the desired second moments/correlations:
116  root = sqrt(1.0_prt-m_muxpx*m_muxpx);
117  a1 = m_sigmaX*x/root;
118  a2 = m_sigmaPx*(-m_muxpx*x/root+px);
119  x = a1;
120  px = a2;
121  root = sqrt(1.0_prt-m_muypy*m_muypy);
122  a1 = m_sigmaY*y/root;
123  a2 = m_sigmaPy*(-m_muypy*y/root+py);
124  y = a1;
125  py = a2;
126  root = sqrt(1.0_prt-m_mutpt*m_mutpt);
127  a1 = m_sigmaT*t/root;
128  a2 = m_sigmaPt*(-m_mutpt*t/root+pt);
129  t = a1;
130  pt = a2;
131  }
132  private:
133  amrex::ParticleReal m_sigmaX,m_sigmaY,m_sigmaT;
134  amrex::ParticleReal m_sigmaPx,m_sigmaPy,m_sigmaPt;
135  amrex::ParticleReal m_muxpx,m_muypy,m_mutpt;
136  };
137 
138 } // namespace distribution
139 } // namespace impactx
140 
141 #endif // IMPACTX_DISTRIBUTION_KURTH4D
#define AMREX_FORCE_INLINE
#define AMREX_GPU_HOST_DEVICE
constexpr std::enable_if_t< std::is_floating_point< T >::value, T > pi()
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE GpuComplex< T > log(const GpuComplex< T > &a_z) noexcept
Real Random()
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE GpuComplex< T > pow(const GpuComplex< T > &a_z, const T &a_y) noexcept
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE GpuComplex< T > sqrt(const GpuComplex< T > &a_z) noexcept
Definition: ImpactX.cpp:32
c
Definition: Kurth4D.H:24
Kurth4D(amrex::ParticleReal const sigx, amrex::ParticleReal const sigy, amrex::ParticleReal const sigt, amrex::ParticleReal const sigpx, amrex::ParticleReal const sigpy, amrex::ParticleReal const sigpt, amrex::ParticleReal const muxpx=0.0, amrex::ParticleReal const muypy=0.0, amrex::ParticleReal const mutpt=0.0)
Definition: Kurth4D.H:35
amrex::ParticleReal m_sigmaX
Definition: Kurth4D.H:133
amrex::ParticleReal m_sigmaY
Definition: Kurth4D.H:133
amrex::ParticleReal m_sigmaPx
related RMS sizes (length)
Definition: Kurth4D.H:134
amrex::ParticleReal m_sigmaPy
Definition: Kurth4D.H:134
amrex::ParticleReal m_sigmaPt
Definition: Kurth4D.H:134
amrex::ParticleReal m_muxpx
RMS momentum.
Definition: Kurth4D.H:135
amrex::ParticleReal m_sigmaT
Definition: Kurth4D.H:133
amrex::ParticleReal m_mutpt
Definition: Kurth4D.H:135
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void operator()(amrex::ParticleReal &x, amrex::ParticleReal &y, amrex::ParticleReal &t, amrex::ParticleReal &px, amrex::ParticleReal &py, amrex::ParticleReal &pt, amrex::RandomEngine const &engine) const
Definition: Kurth4D.H:57
amrex::ParticleReal m_muypy
Definition: Kurth4D.H:135