Setting laser particle positions to be time-centered for implicit sol…

…vers (ECP-WarpX#5485)

The current deposition schemes expect the particle positions to be
time-centered when using the implicit solvers. This is not currently the
case for the laser particles. This PR fixes this issue.

It should be commented that there is really no need for the current
deposition schemes to expect the particle positions to be time centered
for the implicit solvers. This is somewhat of a legacy thing from
PICNIC. This can and should be changed in a future PR.

Here are results of Ey generated from the analysis script for the 1D CI
test using the semi-implicit method:

![plt_Ey](https://github.com/user-attachments/assets/6c925872-66e0-4d7c-85ac-94800d49c71d)

Here are results of Ey generated from the analysis script for the 2D CI
test using the semi-implicit method:

![plt_Ey](https://github.com/user-attachments/assets/32813bba-1074-4beb-85f8-da9289436c32)

Here are results generated from the analysis script for the 3D CI test
using the semi-implicit method:

![laser_analysis](https://github.com/user-attachments/assets/0e3a8505-a039-4e79-99d1-496ff23cd498)

Examples/Tests/laser_injection/CMakeLists.txt

@@ -30,3 +30,23 @@ add_warpx_test(
     diags/diag1000020  # output
     OFF  # dependency
 )
+
+add_warpx_test(
+    test_1d_laser_injection_implicit  # name
+    1  # dims
+    2  # nprocs
+    inputs_test_1d_laser_injection_implicit  # inputs
+    analysis_1d.py  # analysis
+    diags/diag1000240  # output
+    OFF  # dependency
+)
+
+add_warpx_test(
+    test_2d_laser_injection_implicit  # name
+    2  # dims
+    2  # nprocs
+    inputs_test_2d_laser_injection_implicit  # inputs
+    analysis_2d.py  # analysis
+    diags/diag1000240  # output
+    OFF  # dependency
+)

Examples/Tests/laser_injection/inputs_test_1d_laser_injection_implicit

@@ -0,0 +1,79 @@
+# Maximum number of time steps
+max_step = 240
+
+# number of grid points
+amr.n_cell =  352
+
+# Maximum allowable size of each subdomain in the problem domain;
+#    this is used to decompose the domain for parallel calculations.
+amr.max_grid_size = 32
+
+# Maximum level in hierarchy (for now must be 0, i.e., one level in total)
+amr.max_level = 0
+
+# Geometry
+geometry.dims = 1
+geometry.prob_lo     = -15.e-6    # physical domain
+geometry.prob_hi     =  15.e-6
+
+boundary.field_lo = pec
+boundary.field_hi = pec
+
+warpx.serialize_initial_conditions = 1
+
+# Verbosity
+warpx.verbose = 1
+
+# Algorithms
+algo.current_deposition = esirkepov
+warpx.use_filter = 0
+
+# implicit evolve scheme
+algo.evolve_scheme = "semi_implicit_em"
+#
+implicit_evolve.nonlinear_solver = "newton"
+newton.verbose = true
+newton.max_iterations = 21
+newton.relative_tolerance = 1.0e-8
+newton.require_convergence = true
+#
+gmres.verbose_int = 2
+gmres.max_iterations = 1000
+gmres.relative_tolerance = 1.0e-4
+
+# CFL
+warpx.cfl = 0.9
+
+# Order of particle shape factors
+algo.particle_shape = 1
+
+# Laser
+lasers.names        = laser1
+laser1.profile      = Gaussian
+laser1.position     = 0.e-6  0.e-6  0.e-6 # This point is on the laser plane
+laser1.direction    = 0.  0.  1.           # The plane normal direction
+laser1.polarization = 1. 1.  0.           # The main polarization vector
+laser1.e_max        = 4.e12                # Maximum amplitude of the laser field (in V/m)
+laser1.wavelength   = 1.0e-6               # The wavelength of the laser (in meters)
+laser1.profile_waist = 5.e-6               # The waist of the laser (in meters)
+laser1.profile_duration = 10.e-15          # The duration of the laser (in seconds)
+laser1.profile_t_peak = 24.e-15            # The time at which the laser reaches its peak (in seconds)
+laser1.profile_focal_distance = 13.109e-6  # Focal distance from the antenna (in meters)
+                                           #     With this focal distance the laser is at focus
+                                           #     at the end of the simulation.
+
+# Diagnostics
+diagnostics.diags_names = diag1 openpmd
+diag1.intervals = 20
+diag1.diag_type = Full
+
+openpmd.intervals = 20
+openpmd.diag_type = Full
+openpmd.format = openpmd
+
+# Moving window
+warpx.do_moving_window = 1
+warpx.moving_window_dir = z
+warpx.moving_window_v = 1.0 # in units of the speed of light
+warpx.start_moving_window_step = 20
+warpx.end_moving_window_step = 200

Examples/Tests/laser_injection/inputs_test_2d_laser_injection_implicit

@@ -0,0 +1,75 @@
+# Maximum number of time steps
+max_step = 240
+
+# number of grid points
+amr.n_cell =  480 352
+
+# Maximum allowable size of each subdomain in the problem domain;
+#    this is used to decompose the domain for parallel calculations.
+amr.max_grid_size = 32
+
+# Maximum level in hierarchy (for now must be 0, i.e., one level in total)
+amr.max_level = 0
+
+# Geometry
+geometry.dims = 2
+geometry.prob_lo     = -20.e-6    -15.e-6    # physical domain
+geometry.prob_hi     =  20.e-6     15.e-6
+
+boundary.field_lo = pec periodic
+boundary.field_hi = pec periodic
+
+warpx.serialize_initial_conditions = 1
+
+# Verbosity
+warpx.verbose = 1
+
+# Algorithms
+algo.current_deposition = esirkepov
+warpx.use_filter = 0
+
+# implicit evolve scheme
+algo.evolve_scheme = "semi_implicit_em"
+#
+implicit_evolve.nonlinear_solver = "newton"
+newton.verbose = true
+newton.max_iterations = 21
+newton.relative_tolerance = 1.0e-8
+newton.require_convergence = true
+#
+gmres.verbose_int = 2
+gmres.max_iterations = 1000
+gmres.relative_tolerance = 1.0e-4
+
+# CFL
+warpx.cfl = 1.0
+
+# Order of particle shape factors
+algo.particle_shape = 1
+
+# Laser
+lasers.names        = laser1
+laser1.profile      = Gaussian
+laser1.position     = 10.e-6  0.e-6  0.e-6 # This point is on the laser plane
+laser1.direction    = 2.  0.  1.           # The plane normal direction
+laser1.polarization = 1. 1.  -2.           # The main polarization vector
+laser1.e_max        = 4.e12                # Maximum amplitude of the laser field (in V/m)
+laser1.wavelength   = 1.0e-6               # The wavelength of the laser (in meters)
+laser1.profile_waist = 5.e-6               # The waist of the laser (in meters)
+laser1.profile_duration = 10.e-15          # The duration of the laser (in seconds)
+laser1.profile_t_peak = 24.e-15            # The time at which the laser reaches its peak (in seconds)
+laser1.profile_focal_distance = 13.109e-6  # Focal distance from the antenna (in meters)
+                                           #     With this focal distance the laser is at focus
+                                           #     at the end of the simulation.
+
+# Diagnostics
+diagnostics.diags_names = diag1
+diag1.intervals = 240
+diag1.diag_type = Full
+
+# Moving window
+warpx.do_moving_window = 1
+warpx.moving_window_dir = x
+warpx.moving_window_v = 1.0 # in units of the speed of light
+warpx.start_moving_window_step = 20
+warpx.end_moving_window_step = 200

Regression/Checksum/benchmarks_json/test_1d_laser_injection_implicit.json

@@ -0,0 +1,13 @@
+{
+  "lev=0": {
+    "Bx": 374596.7817425552,
+    "By": 374596.7817425552,
+    "Bz": 0.0,
+    "Ex": 111502789524279.0,
+    "Ey": 111502789524279.0,
+    "Ez": 0.0,
+    "jx": 73098054407.2772,
+    "jy": 73098054407.2772,
+    "jz": 0.0
+  }
+}

Regression/Checksum/benchmarks_json/test_2d_laser_injection_implicit.json

@@ -0,0 +1,13 @@
+{
+  "lev=0": {
+    "Bx": 19699314.38858362,
+    "By": 101297372.8536657,
+    "Bz": 39796093.072294116,
+    "Ex": 1.3881256464656438e+16,
+    "Ey": 1.322100107139857e+16,
+    "Ez": 2.6833518029118908e+16,
+    "jx": 3.669364941403736e+16,
+    "jy": 3.669364586262695e+16,
+    "jz": 7.338729883115621e+16
+  }
+}

Source/Particles/LaserParticleContainer.cpp

@@ -917,11 +917,13 @@ LaserParticleContainer::update_laser_particle (WarpXParIter& pti,
             puyp[i] = gamma * vy;
             puzp[i] = gamma * vz;
 
-            // Push the the particle positions
+            // Push the particle positions
 
             // When using the implicit solver, this function is called multiple times per timestep
             // (within the linear and nonlinear solver). Thus, the position of the particles needs to be reset
-            // to the initial position (at the beginning of the timestep), before updating the particle position
+            // to the initial position (at the beginning of the timestep), before updating the particle position.
+            // Also, the current deposition schemes expect the particle positions to be time centered
+            // (cur_time + 0.5*dt) for PushType::Implicit.
 
             ParticleReal x=0., y=0., z=0.;
             if (push_type == PushType::Explicit) {
@@ -930,20 +932,26 @@ LaserParticleContainer::update_laser_particle (WarpXParIter& pti,
 
 #if !defined(WARPX_DIM_1D_Z)
             if (push_type == PushType::Implicit) {
-                x = x_n[i];
+                x = x_n[i] + vx * dt*0.5_prt;
+            }
+            else {
+                x += vx * dt;
             }
-            x += vx * dt;
 #endif
 #if defined(WARPX_DIM_3D) || defined(WARPX_DIM_RZ)
             if (push_type == PushType::Implicit) {
-                y = y_n[i];
+                y = y_n[i] + vy * dt*0.5_prt;
+            }
+            else {
+                y += vy * dt;
             }
-            y += vy * dt;
 #endif
             if (push_type == PushType::Implicit) {
-                z = z_n[i];
+                z = z_n[i] + vz * dt*0.5_prt;
+            }
+            else {
+                z += vz * dt;
             }
-            z += vz * dt;
 
             SetPosition(i, x, y, z);
         }