def fdelx(
vpara, v, vi, B, e, Egg
): # time the electron moves (De/v), angular vel (v/R), speed of el (v,vi) , mag field B, charge e (+/- 1)
# w2,tau2=w,tau
if gv.STODE == 1:
w2 = gv.drawMFPe(Egg, gv.zE(gv.dS)) / v
else:
w2 = gv.De(gv.zE(gv.dS), gv.Ee(Egg, gv.zE(gv.dS))) / v
tau2 = v * 1.0 / gv.R(gv.Ee(Egg, gv.zE(gv.dS)), gv.B0, gv.zE(gv.dS))
return v * (vpara * (tau2 - np.sin(w2 * tau2) / w2) * B +
vi * np.sin(w2 * tau2) / w2 + e *
(np.cos(w2 * tau2) - 1.0) * np.cross(B, vi) / w2)
def F(angles):
x, y, z = getxyzB(dg, dE, angles)
fB = B(x, y, z)
bnorm = np.sqrt(fB[0] * fB[0] + fB[1] * fB[1] + fB[2] * fB[2] + 1e-20)
if RnB:
w = bnorm / (RnB * 1e-14)
else:
w = 1.0 / gv.R(gv.Ee(Egg, gv.zE(gv.dS)), bnorm, gv.zE(gv.dS))
wtau = w * tau
cons1 = fLoS(angles[0], angles[2], dg, dE)
cons2 = fvcBdphi(
fBz(fB, angles[0], angles[1]),
fBrho(fB, angles[0], angles[1]),
angles[2],
angles[0],
)
cons3 = fdeltaEqn(angles[2],
fvpara(fB / bnorm, angles[0], angles[1], angles[2]),
Egg, wtau)
return (cons1, cons2, cons3)
def fsolvecsq_stable(
dg,
dE,
Egg,
tG,
pG,
deltaG,
ranget,
Morp=False,
xtol=1e-10,
tau=False,
RnB=False
): # Solves the Constraints - quite stable, but can jump to other branches
anglesG = np.array([tG, pG, deltaG])
x, y, z = getxyzB(dg, dE, anglesG)
if not tau:
if gv.STODE == 1 and not Morp:
tau = gv.drawMFPe(Egg, gv.zE(gv.dS))
else:
tau = gv.De(gv.zE(gv.dS), gv.Ee(Egg, gv.zE(gv.dS)))
w = 1.0 / gv.R(gv.Ee(Egg, gv.zE(gv.dS)), gv.B0, gv.zE(gv.dS))
wtau = w * tau
def F(angles):
x, y, z = getxyzB(dg, dE, angles)
fB = B(x, y, z)
bnorm = np.sqrt(fB[0] * fB[0] + fB[1] * fB[1] + fB[2] * fB[2] + 1e-20)
if RnB:
w = bnorm / (RnB * 1e-14)
else:
w = 1.0 / gv.R(gv.Ee(Egg, gv.zE(gv.dS)), bnorm, gv.zE(gv.dS))
wtau = w * tau
cons1 = fLoS(angles[0], angles[2], dg, dE)
cons2 = fvcBdphi(
fBz(fB, angles[0], angles[1]),
fBrho(fB, angles[0], angles[1]),
angles[2],
angles[0],
)
cons3 = fdeltaEqn(angles[2],
fvpara(fB / bnorm, angles[0], angles[1], angles[2]),
Egg, wtau)
return (cons1, cons2, cons3)
sol, o1, ier, o2 = opt.fsolve(F, anglesG, xtol=xtol, full_output=1)
charge = 1 # initialize the charge variable, now look what charge this has to be.
if gv.chargeanalyze == 1:
xvec = getxyz(dg, dE, sol)
Bvec = B(xvec[0], xvec[1], xvec[2] + dE)
orientation = np.dot(xvec, np.cross(fvi(sol[0], sol[1], sol[2]), Bvec))
temp = np.dot(Bvec, fvi(sol[0], sol[1], sol[2])) / np.linalg.norm(Bvec)
r = int(np.floor(wtau / (np.pi * np.power(1 - temp * temp, 0.5)))) % 2
if orientation >= 0: # the electron initially moves towards us
if r == 0: # electron must be the lepton
charge = -1
else: # positron must be the lepton
charge = 1
if orientation < 0: # the electron initially moves away from us
if r == 0: # positron must be the lepton
charge = 1
else: # electron must be the lepton
charge = -1
return sol, ier, charge