109 lines
3.0 KiB
Python
109 lines
3.0 KiB
Python
#!/usr/bin/python3
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import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib import rc
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rc('font',**{'family':'serif','serif':['Computer Modern']})
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rc('text', usetex=True)
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e = 1.602176565e-19 #osnovni naboj [C]
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m_pr = 1.672621777e-27 #masa protona [kg]
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m_el = 9.10938291e-31 #masa elektrona [kg]
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c = 299792458 #hitrost svetlobe [m/s]
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def boris(x0, v0, E, B, dt, tdur, q=1, m=1):
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''' Borisov algoritem zabjega skoka za
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integracijo diferencialne enačbe
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x0 = [x,y,z] : vektor zacetne pozicije
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v0 = [vx,vy,vz] : vektor zacetne hitrosti
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E : funkcija, ki daje jakost polja E(x)
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B : funkcija, ki daje jakost polja B(x)
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dt: casovni korak '''
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duration = int(tdur/dt)
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X = np.zeros((duration,3))
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V = np.zeros((duration,3))
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x = x0
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v = v0
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q_prime = dt * q * 0.5 / m
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# https://en.wikipedia.org/wiki/Particle-in-cell
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for time in range(duration):
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h = q_prime*B(x)
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s = 2*h / (1+np.dot(h,h))
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u = v + q_prime*E(x)
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u_ = u + np.cross(u+np.cross(u,h),s)
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v = u_ + q_prime * E(x)
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x = x + dt*v
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V[time,:] = v
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X[time,:] = x
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return X, V
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def B_zemlja(x):
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''' model zemljinega magnentnega polja aproksimiran z
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magnetnim dipolom '''
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B0 = 3.07e-5 # [T]
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Rz = 6378137 # radii zemlje [m]
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r = np.sqrt(np.sum(x**2))
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k = -B0*Rz**3/r**5
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return k*np.array([3*x[0]*x[2],3*x[1]*x[2],2*x[2]**2-x[0]**2-x[1]**2])
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def Wk(m,V):
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return 0.5*m*np.sum(V**2,1)
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def plot3(X,enote='m',zemlja=False):
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fig = plt.figure()
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ax = fig.add_subplot(projection='3d')
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if zemlja:
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u = np.linspace(0, 2 * np.pi, 100)
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v = np.linspace(0, np.pi, 100)
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x = np.outer(np.cos(u), np.sin(v))
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y = np.outer(np.sin(u), np.sin(v))
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z = np.outer(np.ones(np.size(u)), np.cos(v))
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ax.plot_surface(x,y,z,zorder=-4)
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#ax.set_box_aspect(np.ptp(X,axis=0))
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ax.plot(X[:,0],X[:,1],X[:,2],zorder=4)
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ax.set_xlabel(r'$x$ [{}]'.format(enote))
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ax.set_ylabel(r'$y$ [{}]'.format(enote))
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ax.set_zlabel(r'$z$ [{}]'.format(enote))
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plt.show()
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def rplot(X, enote='m', xy=[0,1],os='xy', fname=None):
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fig = plt.figure()
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ax = fig.subplots()
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ax.plot(X[:,xy[0]],X[:,xy[1]], 'k')
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ax.grid()
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dx = X[-1,xy[0]]-X[-2,xy[0]]
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dy = X[-1,xy[1]]-X[-2,xy[1]]
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#ax.arrow(X[-1,xy[0]],X[-1,xy[1]],dx,dy,head_width=0.1,head_length=0.2,
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# overhang=0.3, zorder=10,color='k')
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ax.set_xlabel(r'${}$ [{}]'.format(os[0],enote))
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ax.set_ylabel(r'${}$ [{}]'.format(os[1],enote))
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if fname:
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plt.savefig(fname,bbox_inches='tight')
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plt.show()
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if __name__ == "__main__": # testni del kode
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E = lambda x: np.array([0.0,0.2,0.3])
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B = lambda x: np.array([0.,0.0,1.*x[0]])
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x0 = np.array([-1.,0.,0.])
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v0 = np.array([0.,1.,0.])
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dt = 1e-2
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X, V = boris(x0,v0,E,B,dt,20)
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#ax.quiver(X[0:-1:20,0],X[0:-1:20,1],X[0:-1:20,2],V[0:-1:20,0],V[0:-1:20,1],V[0:-1:20,2], color='black',normalize=True,length=.5)
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# quiver res naredi grdo sliko
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plot3(X)
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