def track(self, beam):
"""The formula that describes the transverse kick experienced
by an ultra-relativistic particle traversing the RFQ
longitudinally is based on the thin-lens approximation
\Delta p_x = -x*(2 e v_2 / omega) *
cos(omega z / (beta c) + phi_0),
\Delta p_y = y*(2 e v_2 / omega) *
cos(omega z / (beta c) + phi_0).
"""
cos_term = (2. * e * self.v_2 / self.omega *
pm.cos(self.omega / (beam.beta * c) * beam.z + self.phi_0))
beam.xp += -beam.x * cos_term / beam.p0
beam.yp += beam.y * cos_term / beam.p0
def detune(self, beam):
""" Calculates for each particle its betatron detuning
dQ_x, dQ_y according to formulae taken from [1] (see
above).
dQ_x = dapp_xz / p * \cos(omega / (beta c) z + phi_0)
dQ_y = dapp_yz / p * \cos(omega / (beta c) z + phi_0)
with
dapp_xz = beta_x_RFQ * v_2 * e / (2 Pi * omega)
dapp_yz = -beta_y_RFQ * v_2 * e / (2 Pi * omega)
and p the particle momentum p = (1 + dp) p0.
(Probably, it would make sense to approximate p by p0 for better
performance). """
p = (1. + beam.dp) * beam.p0
cos_term = pm.cos(self.omega /
(beam.beta * c) * beam.z + self.phi_0) / p
dQ_x = self.dapp_xz * cos_term
dQ_y = self.dapp_yz * cos_term
return dQ_x, dQ_y