From 145136f70c27664ab94d470bde5ffd6e26146380 Mon Sep 17 00:00:00 2001
From: Andrej <andrej@baza>
Date: Fri, 4 Jun 2021 19:38:26 +0200
Subject: [PATCH] prvi delujoc primer implementacije borisa

---
 boris.py | 55 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 55 insertions(+)

diff --git a/boris.py b/boris.py
index a93a4bf..c3619d3 100644
--- a/boris.py
+++ b/boris.py
@@ -1 +1,56 @@
 #!/usr/bin/python3
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib import rc
+rc('font',**{'family':'serif','serif':['Computer Modern']})
+rc('text', usetex=True)
+
+Q = 1.602176565e-19
+
+def boris(x0, v0, E, B, dt, q=1, m=1):
+    ''' Borisov algoritem zabjega skoka za
+    integracijo diferencialne enačbe
+
+    x0 = [x,y,z] : vektor zacetne pozicije
+    v0 = [vx,vy,vz] : vektor zacetne hitrosti
+    E : funkcija, ki daje jakost polja E(x)
+    B : funkcija, ki daje jakost polja B(x)
+    dt: casovni korak '''
+
+    duration = 1000
+
+    X = np.zeros((duration,3))
+    V = np.zeros((duration,3))
+    x = x0
+    v = v0
+
+    q_prime = dt * q * 0.5 / m
+    
+    # https://en.wikipedia.org/wiki/Particle-in-cell
+    for time in range(duration):
+        h = q_prime*B(x)
+        s = 2*h / (1+np.dot(h,h))
+        u = v + q_prime*E(x)
+        u_ = u + np.cross(u+np.cross(u,h),s)
+        
+        v = u_ + q_prime * E(x)
+        x = x + dt*v
+        V[time,:] = v
+        X[time,:] = x
+
+    return X, V
+
+E = lambda x: np.array([0.0,0.0,0.])
+B = lambda x: np.array([0.,0.0,1.*x[0]])
+
+x0 = np.array([-1.,0.,0.])
+v0 = np.array([0.,1.,0.])
+
+dt = 1e-2
+
+X, V = boris(x0,v0,E,B,dt)
+
+ax = plt.figure().add_subplot(projection='3d')
+ax.plot(X[:,0],X[:,1],X[:,2])
+plt.xlabel(r'$x$ label')
+plt.show()