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popravil polje zanke in singularnosti v osi

master
Andrej 2021-06-16 09:34:24 +02:00
parent 9515e50859
commit f94f50b282
3 changed files with 18 additions and 11 deletions
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__pycache__/boris.cpython-37.pyc
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boris.py
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@ -57,16 +57,20 @@ def B_zemlja(x):
def B_loop(p, a): def B_loop(p, a):
''' polje magnetne zanke polmera a v xy ravnini, normiran tok 1A ''' polje magnetne zanke polmera a v xy ravnini, normiran tok 1A
glej: Sinigoj, ELMG polje, stran 200''' glej: Sinigoj, ELMG polje, stran 200'''
mu = 1e-7 # mu/4/pi mu = 2e-7 # mu/2/pi
x,y,z = p x,y,z = p
r = np.sqrt(x**2+y**2) r = np.sqrt(x**2+y**2)
R0 = np.sqrt((r+a)**2+z**2) if r < 1e-15:
Bz = 2*np.pi*1e-7*a**2/(a**2+z**2)**1.5
return np.array([0.,0.,Bz])
m = 4*a*r/( (r+a)**2+z**2) m = 4*a*r/( (r+a)**2+z**2)
K = ellipk(m) K = ellipk(m)
E = ellipe(m) E = ellipe(m)
Br = -mu * z/r/R0 * (2*K - (2-m)*E/(1-m)) C = 1./np.sqrt((a+r)**2+z**2)
Bz = mu/R0 * (2*K - (2-m*(r+a)/r)*E/(1-m))
Br = -mu * z/r*C * (-K + (a**2+r**2+z**2)*E/((a-r)**2+z**2))
Bz = mu*C * (K - (a**2-r**2-z**2)*E/((a-r)**2+z**2))
return np.array([Br*x/r, Br*y/r, Bz]) return np.array([Br*x/r, Br*y/r, Bz])
@ -106,20 +110,19 @@ def tokamak(p, a, b, I, n):
''' polje v modelu tokamaka, zanke polmera a ''' polje v modelu tokamaka, zanke polmera a
nataknjene na toroid polmera b ''' nataknjene na toroid polmera b '''
z_obrat = np.array([[1.,0.,0.],[0.,0.,1.],[0.,-1.,0.]]) z_obrat = np.array([[1.,0.,0.],[0.,0.,1.],[0.,-1.,0.]])
v0 = np.array([0.,0.,.1]) B = np.zeros(3)
B = np.zeros([1,3]) premik = np.array([b,0.,0.])
for i in range(n): for i in range(n):
theta = i*2.*np.pi/n theta = i*2.*np.pi/n
x_obrat = np.array([[np.cos(theta), np.sin(theta),0.], x_obrat = np.array([[np.cos(theta), np.sin(theta),0.],
[-np.sin(theta),np.cos(theta), 0.], [-np.sin(theta),np.cos(theta), 0.],
[0.,0.,0.2]]) [0.,0.,0.2]])
p_ = np.matmul(x_obrat, np.matmul(z_obrat,p)) - np.array([b,0.,0.]) p_ = np.matmul(x_obrat, np.matmul(z_obrat,p)) - premik
b_ = I*B_loop(p_,a) b_ = I*B_loop(p_,a)
b = np.matmul(x_obrat, np.matmul(z_obrat,b_)) b = np.matmul(z_obrat.T, np.matmul(x_obrat.T,b_))
B = B+b B = B+b
print(B)
return B return B
def Wk(m,V): def Wk(m,V):

8
tokamak.py
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@ -17,11 +17,15 @@ a = 1.5 # ovoj
b = 0.8 + 0.5*a b = 0.8 + 0.5*a
v0 = np.array([-0.1,-0.15,0.])*c v0 = np.array([-0.1,-0.15,0.])*c
v0 = np.array([0.8, -0.48, 0.3595])*c
x0 = np.array([2.3, 0.,0.]) x0 = np.array([2.3, 0.,0.])
x0 = np.array([0.,0.,0.8])
E = lambda x: np.array([0.,0.,0.]) E = lambda x: np.array([0.,0.,0.])
B = lambda x: tokamak(x, a, b, I, 16) B = lambda x: tokamak(x, a, b, I, 16)
B = lambda x: B_bottle(x, 1., 5., I)
dt = 2e-11 dt = 2e-11
tdur = 1e-7 tdur = 1e-6
print(tdur/dt) #print(tdur/dt)
X,V = boris(x0, v0, E, B, dt, tdur, q, m) X,V = boris(x0, v0, E, B, dt, tdur, q, m)
plot3(X)