def mu(self):
"""Return a 1-d array of the magnetic moment values along the trajectory."""
out = []
for row in self.trajectory:
t, r, mom = row[0], row[1:4], row[4:]
gm = np.sqrt(self.mass**2 + np.dot(mom,mom)/c**2) # gamma * mass
v = mom/gm
rgc, vp, spd = ru.guidingcenter(t, r, v, self.field, self.mass, self.charge)
out.append(ru.magnetic_moment(t, rgc, vp, spd, self.field, self.mass))
return np.array(out)
def guidingcenter(self):
"""Return a 2-d array of guiding center positions corresponding to particle positions."""
out = []
for row in self.trajectory:
t,r,mom = row[0], row[1:4], row[4:]
gm = np.sqrt(self.mass**2 + np.dot(mom,mom)/c**2) # gamma * mass
v = mom/gm
rgc, vp, spd = ru.guidingcenter(t, r, v, self.field, self.mass, self.charge)
out.append(list(rgc)+[vp,spd])
return np.array(out)
def init(self, p):
"""
Initialize a Particle using the state of another Particle or GuidingCenter object.
Parameters
-----------
p : Particle or GuidingCenter object.
The object that is used to initialize the current GuidingCenter.
Notes
-----
Takes the last state (position and momentum) of the given `Particle`
or `GuidingCenter`, sets the initial conditions of self to match them,
and runs `__init__` again. Therefore, all existing data is erased.
"""
from rapt import Particle # Import here to avoid circular imports.
if isinstance(p, GuidingCenter):
B = p.field.magB(p.trajectory[-1,:4])
gamma = np.sqrt(1 + 2*p.mu*B/(p.mass*c*c) + (p.trajectory[-1,4]/p.mass/c)**2)
if gamma-1 < 1e-6: # nonrelativistic
v = np.sqrt(2*p.mu*B/p.mass + (p.trajectory[-1,4]/p.mass)**2)
else:
v = c * np.sqrt(1-1/gamma**2)
self.__init__(pos = p.trajectory[-1,1:4],
v = v,
ppar = p.trajectory[-1,4],
t0 = p.trajectory[-1,0],
mass = p.mass,
charge = p.charge,
field = p.field)
self.check_adiabaticity = p.check_adiabaticity
elif isinstance(p, Particle):
mom = p.trajectory[-1,4:]
gm = np.sqrt(p.mass**2 + np.dot(mom,mom)/c**2) # gamma * m
vel = mom/gm # velocity
pos, vp, v = ru.guidingcenter(p.trajectory[-1,0],
p.trajectory[-1,1:4],
vel,
p.field,
p.mass,
p.charge)
gamma = 1 / np.sqrt(1-(v/c)**2)
self.__init__(pos = pos,
v = v,
ppar = p.mass*gamma*vp,
t0 = p.trajectory[-1,0],
mass = p.mass,
charge = p.charge,
field = p.field)
self.check_adiabaticity = p.check_adiabaticity
else:
raise(ValueError, "Particle or GuidingCenter objects required.")
def init(self, p):
"""
Initialize a Particle using the state of another Particle or GuidingCenter object.
Parameters
-----------
p : Particle or GuidingCenter object.
The object that is used to initialize the current GuidingCenter.
Notes
-----
Takes the last state (position and momentum) of the given `Particle`
or `GuidingCenter`, sets the initial conditions of self to match them,
and runs `__init__` again. Therefore, all existing data is erased.
"""
from rapt import Particle # Import here to avoid circular imports.
if isinstance(p, GuidingCenter):
B = p.field.magB(p.trajectory[-1,:4])
gamma = np.sqrt(1 + 2*p.mu*B/(p.mass*c*c) + (p.trajectory[-1,4]/p.mass/c)**2)
if gamma-1 < 1e-6: # nonrelativistic
v = np.sqrt(2*p.mu*B/p.mass + (p.trajectory[-1,4]/p.mass)**2)
else:
v = c * np.sqrt(1-1/gamma**2)
self.__init__(pos = p.trajectory[-1,1:4],
v = v,
ppar = p.trajectory[-1,4],
t0 = p.trajectory[-1,0],
mass = p.mass,
charge = p.charge,
field = p.field)
self.check_adiabaticity = p.check_adiabaticity
elif isinstance(p, Particle):
mom = p.trajectory[-1,4:]
gm = np.sqrt(p.mass**2 + np.dot(mom,mom)/c**2) # gamma * m
vel = mom/gm # velocity
pos, vp, v = ru.guidingcenter(p.trajectory[-1,0],
p.trajectory[-1,1:4],
vel,
p.field,
p.mass,
p.charge)
gamma = 1 / np.sqrt(1-(v/c)**2)
self.__init__(pos = pos,
v = v,
ppar = p.mass*gamma*vp,
t0 = p.trajectory[-1,0],
mass = p.mass,
charge = p.charge,
field = p.field)
self.check_adiabaticity = p.check_adiabaticity
else:
raise(ValueError, "Particle or GuidingCenter objects required.")
def guidingcenter(self):
"""Return a 2-d array of guiding center positions corresponding to particle positions."""
out = []
for row in self.trajectory:
t, r, mom = row[0], row[1:4], row[4:]
gm = np.sqrt(self.mass**2 +
np.dot(mom, mom) / c**2) # gamma * mass
v = mom / gm
rgc, vp, spd = ru.guidingcenter(t, r, v, self.field, self.mass,
self.charge)
out.append(list(rgc) + [vp, spd])
return np.array(out)
def mu(self):
"""Return a 1-d array of the magnetic moment values along the trajectory."""
out = []
for row in self.trajectory:
t, r, mom = row[0], row[1:4], row[4:]
gm = np.sqrt(self.mass**2 +
np.dot(mom, mom) / c**2) # gamma * mass
v = mom / gm
rgc, vp, spd = ru.guidingcenter(t, r, v, self.field, self.mass,
self.charge)
out.append(
ru.magnetic_moment(t, rgc, vp, spd, self.field, self.mass))
return np.array(out)
