The Equations class

The Equations class is top-level class in KENV. It contains all the equations data, and has the high-level methods envelope_prime, centroid_prime, particle_prime that performs the integrate.

class kenv.solver.Equations(beam, accelerator, particle=<kenv.beam.Particle object>)[source]

Initializes an Equations.

Parameters

  • beam (an instance of Beam) – Beam data

  • accelerator (an instance of Accelerator) – Accelerator data

  • Particle (an instance of Particle, optional) – Particle data

centroid_prime(z: numpy.arange, X: list) → list[source]

Located derivative for further integration Kapchinscky equation for centroid trajectory.

Parameters

  • z (an instance of the np.arange class) – Axis z

  • X (list) – Initial conditions, [x0, xp0, y, yp0, larmor_angle]

envelope_prime(z: numpy.arange, X: list) → list[source]

Located derivative for further integration Kapchinscky equation for envelope beam.

Parameters

  • z (an instance of the np.arange class) – Axis z

  • X (list) – Initial conditions, [x0, xp0, y, yp0]

particle_prime(z: numpy.arange, X: list, envelope_x, envelope_y) → list[source]

Located derivative for further integration Kapchinscky equation for envelope beam.

Parameters

  • z (an instance of the np.arange class) – Axis z

  • X (list) – Initial conditions, [x0, xp0, y, yp0, larmor_angle]