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 __init__(self,
pos=[],
v=None,
t0=0,
pa=None,
mass=None,
charge=None,
field=None):
"""
Object constructor.
Parameters
----------
pos: list or array
The initial position (x,y,z) of the particle, in meters.
v: float
The initial speed of the particle, in m/s.
t0: float
The time of simulation at the beginning (seconds).
pa: float
The initial pitch angle, in degrees
mass: float
The mass of the particle, in kg.
charge: float
The charge of the particle, in Coulombs.
field: Field object
The field object that provides electric and magnetic field vectors and
related quantities.
"""
self.pos = pos # initial position array
self.v = v # speed of the particle
self.t0 = t0
self.tcur = t0 # current time
self.mass = mass # mass of the particle
self.charge = charge # charge of the particle
self.field = field # the field object
self.isequatorial = False
if not field.static:
raise RuntimeError(
"BounceCenter does not work with nonstatic fields or electric fields."
)
return None
# The initial pitch angle:
self.pa = pa
if not (pos == [] or v == None
or pa == None): # if initial state is given explicitly
self.trajectory = np.concatenate(([t0], pos))
self.trajectory = np.reshape(self.trajectory, (1, 4))
# the first invariant value (constant)
self.mu = ru.magnetic_moment(t0, pos, self.v * np.cos(self.pa),
self.v, field, mass)
assert self.mu > 0
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 __init__(self, pos=[], v=None, t0=0, pa=None, mass=None, charge=None, field=None):
"""
Object constructor.
Parameters
----------
pos: list or array
The initial position (x,y,z) of the particle, in meters.
v: float
The initial speed of the particle, in m/s.
t0: float
The time of simulation at the beginning (seconds).
pa: float
The initial pitch angle, in degrees
mass: float
The mass of the particle, in kg.
charge: float
The charge of the particle, in Coulombs.
field: Field object
The field object that provides electric and magnetic field vectors and
related quantities.
"""
self.pos = pos # initial position array
self.v = v # speed of the particle
self.t0 = t0
self.tcur = t0 # current time
self.mass = mass # mass of the particle
self.charge = charge # charge of the particle
self.field = field # the field object
self.isequatorial = False
if not field.static:
raise RuntimeError("BounceCenter does not work with nonstatic fields or electric fields.")
return None
# The initial pitch angle:
self.pa = pa
if not (pos==[] or v==None or pa==None): # if initial state is given explicitly
self.trajectory = np.concatenate(([t0], pos))
self.trajectory = np.reshape(self.trajectory, (1,4))
# the first invariant value (constant)
self.mu = ru.magnetic_moment(t0, pos, self.v*np.cos(self.pa), self.v, field, mass)
assert self.mu>0
def __init__(self, pos=[], v=0, pa=None, ppar=None, t0=0, mass=None, charge=None, field=None):
"""
Object constructor.
Parameters
----------
pos: list or array
The initial position (x,y,z) of the particle, in meters.
v: float
The initial speed of the particle, in m/s.
pa: float
The initial pitch angle, in degrees (not needed if ppar is given)
ppar: float
The initial parallel momentum, in kg m/s (not needed if pa is given)
t0: float
The time of simulation at the beginning (seconds), ignored for fields that do not depend on time.
mass: float
The mass of the particle, in kg.
charge: float
The charge of the particle, in Coulombs.
field: Field object
The field object that provides electric and magnetic field vectors and related quantities.
See Also
--------
init
Notes
-----
All parameters above are optional. The object can be initialized with
an empty parameter set if it is going to be initialized differently
(e.g. with `init` method)
"""
# pos: initial position (array of 3)
# v: initial speed (scalar)
# pa: initial pitch angle
# ppar = initial parallel momentum
# (N.B. Either pa or ppar should be provided. If both given, pa is used.)
# t0: initial time
# mass: particle mass in kg
# charge: particle charge in C
# field: The field object
self.pos = pos # initial position array
self.v = v
self.t0 = t0 # initial time
self.tcur = t0 # current time
self.mass = mass # mass of the particle
self.charge = charge # charge of the particle
self.field = field
self.trajectory = np.zeros((1,5))
self.check_adiabaticity = False
# The object can be initialized two ways:
# Either by specifying the initial conditions,
# or by an empty call, to be initialized later by another object.
# We consider the call empty when pos and v are not specified.
if not (pos==[] or v==0): # if initial state is given explicitly
gamma = 1/np.sqrt(1-(v/c)**2)
if pa != None:
vpar = 0 if pa==90 else v * np.cos(pa*np.pi/180)
ppar = gamma*mass*vpar
self.mu = ru.magnetic_moment(self.tcur, self.pos, ppar/(mass*gamma),
self.v, self.field, self.mass)
self.trajectory[0,0] = t0
self.trajectory[0,1:4] = pos[:]
self.trajectory[0,4] = ppar
def __init__(self, pos=[], v=0, pa=None, ppar=None, t0=0, mass=None, charge=None, field=None):
"""
Object constructor.
Parameters
----------
pos: list or array
The initial position (x,y,z) of the particle, in meters.
v: float
The initial speed of the particle, in m/s.
pa: float
The initial pitch angle, in degrees (not needed if ppar is given)
ppar: float
The initial parallel momentum, in kg m/s (not needed if pa is given)
t0: float
The time of simulation at the beginning (seconds), ignored for fields that do not depend on time.
mass: float
The mass of the particle, in kg.
charge: float
The charge of the particle, in Coulombs.
field: Field object
The field object that provides electric and magnetic field vectors and related quantities.
See Also
--------
init
Notes
-----
All parameters above are optional. The object can be initialized with
an empty parameter set if it is going to be initialized differently
(e.g. with `init` method)
"""
# pos: initial position (array of 3)
# v: initial speed (scalar)
# pa: initial pitch angle
# ppar = initial parallel momentum
# (N.B. Either pa or ppar should be provided. If both given, pa is used.)
# t0: initial time
# mass: particle mass in kg
# charge: particle charge in C
# field: The field object
self.pos = pos # initial position array
self.v = v
self.t0 = t0 # initial time
self.tcur = t0 # current time
self.mass = mass # mass of the particle
self.charge = charge # charge of the particle
self.field = field
self.trajectory = np.zeros((1,5))
self.check_adiabaticity = False
# The object can be initialized two ways:
# Either by specifying the initial conditions,
# or by an empty call, to be initialized later by another object.
# We consider the call empty when pos and v are not specified.
if not (pos==[] or v==0): # if initial state is given explicitly
gamma = 1/np.sqrt(1-(v/c)**2)
if pa != None:
vpar = 0 if pa==90 else v * np.cos(pa*np.pi/180)
ppar = gamma*mass*vpar
self.mu = ru.magnetic_moment(self.tcur, self.pos, ppar/(mass*gamma),
self.v, self.field, self.mass)
self.trajectory[0,0] = t0
self.trajectory[0,1:4] = pos[:]
self.trajectory[0,4] = ppar