Add feedback passmethod

[lcarver]

Adding a simple passmethod to compute the mean position of the full beam and feedback with a gain.

The feedback takes simply a gain in x,y, and z, and an optional closed_orbit array (6d).

In this module, a closed_orbit is needed to make sure that the feedback is working. But this does not dictate what the closed_orbit is. To account for this, I added the orbit6 into at.simple_ring to allow an appropriate closed_orbit to feedback to to check that it is working.

Tested with mpi and without, all working fine.

Below is an example script.

from mpi4py import MPI
import at
import numpy as np 
import matplotlib.pyplot as plt


comm = MPI.COMM_WORLD


size = comm.Get_size()
rank = comm.Get_rank()
rank0 = rank == 0

plane = 2
gx = 0.0
gy = 0.01
gz = 0
orb = 3.e-3

closed_orbit = np.array([0.0, 0, 0, 0, 0, 0])
closed_orbit[plane] = orb



ring = at.simple_ring(6e9, 844, 992, 0.1, 0.18, 6e6, 8.5e-5, orb6=closed_orbit, tauy=0,  emity=0) #no radiation damping
ring.set_fillpattern(1)
sigma_matrix = at.sigma_matrix(betax=1, betay=1, alphax=0, alphay=0, emitx=100e-12, emity=10e-18, espread=1e-3, blength=3e-3)

nparts = 1000
nturns = 10000


fb = at.Feedback('fb', gx,gy,gz, closed_orbit)
ring.append(fb)


bmon = at.BeamMoments('bmon')
ring.append(bmon)


parts = at.beam(nparts, sigma_matrix)
parts[plane,:] += 1e-3

if rank0:
    all_means_fb = np.zeros((6,nturns))

for i in np.arange(nturns):
    ring.track(parts, in_place=True, refpts=None)
    
    if rank0:
        all_means_fb[:,i] = bmon.means[:,0,0]       

if rank0:
    plt.plot(1e3*all_means_fb[plane,:])
    plt.xlabel('Turn')
    plt.ylabel('y pos [mm]')
    plt.suptitle('CO_y = {:.0f}mm'.format(orb*1e3))
    plt.show()

[lcarver]

[swhite2401]

I think in other element we pass num_particles as the last argument but this is cosmetic

[lcarver]

What I put here follows what is in BeamMomentsPass and SliceMomentsPass.

[lcarver]

ready for re-review

[swhite2401]

Isn't is possible to generate a simple ring from just an AT lattice?

[lcarver]

Well, that is typically what fast_ring is for. Simple_ring is more for inputs by hand. But you are right i could pass a lattice and make an even simpler fast_ring from a lattice. That is separate to this though.

[lcarver]

ready for re-re-review

[lcarver]

Please re-approve. I made a last check of my script and realised I had forgotten to change the GX->Gx in the C, as it is optional it was not doing any damping!

[swhite2401]

Please re-approve. I made a last check of my script and realised I had forgotten to change the GX->Gx in the C, as it is optional it was not doing any damping!

Could you please add unit tests first? Thanks!