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pic88.py

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+# Authored by Luhuai Jiao
+import taichi as ti
+
+ti.init(arch=ti.gpu)
+PI = 3.141592653589793
+L = 8 * PI
+dt = 0.1
+substepping = 4
+ng = 32
+np = 16384
+vb = 1.0
+vt = 0.3
+wp = 1  #Plasma frequence
+qm = -1
+q = wp * wp / (qm * np / L)
+rho_back = -q * np / L  #background charge
+dx = L / ng
+inv_dx = 1.0 / dx
+x = ti.Vector.field(1, ti.f32, np)
+v = ti.Vector.field(1, ti.f32, np)
+rho = ti.Vector.field(1, ti.f32, ng)
+e = ti.Vector.field(1, ti.f32, ng)
+v_x_pos1 = ti.Vector.field(2, ti.f32, int(np / 2))  #to plot Vx-X
+v_x_pos2 = ti.Vector.field(2, ti.f32, int(np / 2))
+
+
+@ti.kernel
+def initialize():
+    for p in x:
+        x[p].x = (p + 1) * L / np
+        v[p].x = vt * ti.randn() + (-1)**p * vb
+
+
+@ti.kernel
+def substep():
+    for p in x:
+        x[p] += v[p] * dt
+        if x[p].x >= L:
+            x[p] += -L
+        if x[p].x < 0:
+            x[p] += L
+    rho.fill(rho_back)
+    for p in x:
+        base = (x[p] * inv_dx - 0.5).cast(int)
+        fx = x[p] * inv_dx - 0.5 - base.cast(float)
+        rho[base] += (1.0 - fx) * q * inv_dx
+        rho[base + 1] += fx * q * inv_dx
+    e.fill(0.0)
+    ti.loop_config(serialize=True)
+    for i in range(ng):
+        e[i] = e[i - 1] + (rho[i - 1] + rho[i]) * dx * 0.5
+    s = 0.0
+    for i in e:
+        s += e[i].x
+    for i in e:
+        e[i] += -s / ng
+    for p in v:
+        base = (x[p] * inv_dx - 0.5).cast(int)
+        fx = x[p] * inv_dx - 0.5 - base.cast(float)
+        a = (e[base] * (1.0 - fx) + e[base + 1] * fx) * qm
+        v[p] += a * dt
+
+
+@ti.kernel
+def vx_pos():
+    for p in x:
+        if p % 2:
+            v_x_pos1[int((p - 1) / 2)].x = x[p].x / L
+            v_x_pos1[int((p - 1) / 2)].y = (v[p].x) / 10 + 0.5
+        else:
+            v_x_pos2[int(p / 2)].x = x[p].x / L
+            v_x_pos2[int(p / 2)].y = (v[p].x) / 10 + 0.5
+
+
+def main():
+    initialize()
+    gui = ti.GUI("pic88", (800, 800))
+    while not gui.get_event(ti.GUI.ESCAPE, ti.GUI.EXIT):
+        for s in range(substepping):
+            substep()
+        vx_pos()
+        gui.circles(v_x_pos1.to_numpy(), color=0x0000ff, radius=2)
+        gui.circles(v_x_pos2.to_numpy(), color=0xff0000, radius=2)
+        gui.show()
+
+
+if __name__ == '__main__':
+    main()