"""
Functions relating to fast_ring
"""
from __future__ import annotations
from functools import reduce
import numpy
from typing import Union
from collections.abc import Sequence
from at.lattice import Lattice, Particle
from at.lattice import RFCavity, Element, Marker, get_cells, checkname
from at.lattice import get_elements, M66, SimpleQuantDiff, AtError, SimpleRadiation
from at.physics import gen_m66_elem, gen_detuning_elem, gen_quantdiff_elem
from at.constants import clight
import copy
__all__ = ['fast_ring', 'simple_ring']
def _rearrange(ring: Lattice, split_inds=[]):
inds = numpy.append(split_inds, [0, len(ring)+1])
inds = numpy.unique(inds)
all_rings = [ring[int(b):int(e)] for b, e in zip(inds[:-1], inds[1:])]
ringm = []
for ring_slice in all_rings:
ring_slice.insert(0, Marker('xbeg'))
ring_slice.append(Marker('xend'))
cavs = [e for e in ring_slice if isinstance(e, RFCavity)]
newpass = ['IdentityPass' if c.Length == 0
else 'DriftPass' for c in cavs]
for c, pm in zip(cavs, newpass):
c.PassMethod = pm
uni_freq = numpy.unique([e.Frequency for e in cavs])
for fr in numpy.atleast_1d(uni_freq):
cavf = [c for c in cavs if c.Frequency == fr]
vol = reduce(lambda x, y: x+y, (c.Voltage for c in cavf))
cavl = RFCavity('CAVL', 0, vol, fr,
cavf[0].HarmNumber, cavf[0].Energy)
cavl.TimeLag = cavf[0].TimeLag
ring_slice.append(cavl)
ringm = ringm + ring_slice
return all_rings, Lattice(ringm, energy=ring.energy)
def _fring(ring, split_inds=[], detuning_elem=None):
all_rings, merged_ring = _rearrange(ring, split_inds=split_inds)
ibegs = get_cells(merged_ring, checkname('xbeg'))
iends = get_cells(merged_ring, checkname('xend'))
_, orbit = merged_ring.find_orbit(refpts=ibegs | iends)
if detuning_elem is None:
detuning_elem = gen_detuning_elem(merged_ring, orbit[-1])
else:
detuning_elem.T1 = -orbit[-1]
detuning_elem.T2 = orbit[-1]
fastring = []
for counter, r in enumerate(all_rings):
cavs = [e for e in r if e.PassMethod.endswith('CavityPass')]
[r.remove(c) for c in cavs]
lin_elem = gen_m66_elem(r, orbit[2*counter],
orbit[2*counter+1])
lin_elem.FamName = lin_elem.FamName + '_' + str(counter)
[fastring.append(c) for c in cavs]
fastring.append(lin_elem)
fastring.append(detuning_elem)
try:
qd_elem = gen_quantdiff_elem(merged_ring)
fastring.append(qd_elem)
except ValueError: # No synchrotron radiation => no diffusion element
pass
fastring = Lattice(fastring, **vars(ring))
return fastring
[docs]
def fast_ring(ring: Lattice, split_inds=[]) -> tuple[Lattice, Lattice]:
"""Generates a "fast ring"
A fast ring consisting in:
* a RF cavity per distinct frequency,
* a 6x6 linear transfer map,
* a detuning and chromaticity element,
* a quantum diffusion element (for radiation ring).
2 new lattices are returned, one with radiation and one without
It is possible to split the original ring in multiple "fastrings"
using the ``split_inds`` argument
Parameters:
ring: Lattice description
split_inds: List of indexes where to split the ring
Returns:
fring (Lattice): Fast ring without radiation
fringrad (Lattice): Fast ring with radiation
"""
ringi = ring.deepcopy()
fastringnorad = _fring(ringi.radiation_off(copy=True),
split_inds=split_inds)
detuning_elem = copy.deepcopy(get_elements(fastringnorad,
'NonLinear')[0])
fastringrad = _fring(ringi.radiation_on(copy=True),
split_inds=split_inds,
detuning_elem=detuning_elem)
return fastringnorad, fastringrad
[docs]
def simple_ring(energy: float, circumference: float,
harmonic_number: Union[float, Sequence[float]],
Qx: float, Qy: float,
Vrf: Union[float, Sequence[float]],
alpha: float,
betax: float = 1.0, betay: float = 1.0,
alphax: float = 0.0, alphay: float = 0.0,
dispx: float = 0.0, dispxp: float = 0.0,
dispy: float = 0.0, dispyp: float = 0.0,
Qpx: float = 0.0, Qpy: float = 0.0,
A1: float = 0.0, A2: float = 0.0,
A3: float = 0.0, emitx: float = 0.0,
emity: float = 0.0, espread: float = 0.0,
taux: float = 0.0, tauy: float = 0.0,
tauz: float = 0.0, U0: float = 0.0,
name: str = "",
particle: Union[str, Particle] = 'relativistic',
TimeLag: Union[float, Sequence[float]] = 0.0,
) -> Lattice:
"""Generates a "simple ring" based on a given dictionary
of global parameters
A simple ring consists of:
* an RF cavity,
* a 6x6 linear transfer map with no radiation damping,
* a detuning and chromaticity element,
* a simple radiation damping element
* a simplified quantum diffusion element which contains equilibrium emittance
Parameters:
energy: [eV]
circumference: [m]
harmonic_number: can be scalar or sequence of scalars. The RF
frequency is derived from this and the ring circumference
Qx: horizontal tune
Qy: vertical tune
Vrf: RF Voltage set point [V] - can be scalar or sequence of scalars
alpha: momentum compaction factor
betax: horizontal beta function [m], Default=1
betay: vertical beta function [m], Default=1
alphax: horizontal alpha function, Default=0
alphay: vertical alpha function, Default=0
dispx: horizontal dispersion [m], Default=0
dispxp: horizontal dispersion prime, Default=0
dispy: vertical dispersion [m], Default=0
dispyp: vertical dispersion prime, Default=0
Qpx: horizontal linear chromaticity, Default=0
Qpy: vertical linear chromaticity, Default=0
A1: horizontal amplitude detuning coefficient, Default=0
A2: cross term for amplitude detuning coefficient, Default=0
A3: vertical amplitude detuning coefficient, Default=0
emitx: horizontal equilibrium emittance [m.rad], Default=0
ignored if emitx=0
emity: vertical equilibrium emittance [m.rad], Default=0
ignored if emity=0
espread: equilibrium momentum spread, Default=0
ignored if espread=0
taux: horizontal radiation damping time [turns], Default=0
ignored if taux=0
tauy: vertical radiation damping time [turns], Default=0
ignored if tauy=0
tauz: longitudinal radiation damping time [turns], Default=0
ignored if tauz=0
U0: energy loss [eV] (positive number), Default=0
name: Name of the lattice
particle: circulating particle. May be
'relativistic', 'electron', 'positron', 'proton'
or a Particle object
TimeLag: Set the timelag of the cavities, Default=0. Can be scalar
or sequence of scalars (as with harmonic_number and Vrf).
If the given emitx, emity or espread is 0, then no equlibrium emittance
is applied in this plane.
If the given tau is 0, then no radiation damping is applied for this plane.
Returns:
ring: Simple ring
"""
try:
rfp = numpy.broadcast(Vrf, harmonic_number, TimeLag)
except ValueError:
raise AtError('Vrf, harmonic_number and TimeLag must be broadcastable')
# revolution frequency
f0 = clight / circumference
all_cavities = [RFCavity(f"RFC{i+1}", 0.0, v, h*f0, h, energy, TimeLag=t)
for i, (v, h, t) in enumerate(rfp)]
# Now we will use the optics parameters to compute the uncoupled M66 matrix
s_dphi_x = numpy.sin(2*numpy.pi*Qx)
c_dphi_x = numpy.cos(2*numpy.pi*Qx)
s_dphi_y = numpy.sin(2*numpy.pi*Qy)
c_dphi_y = numpy.cos(2*numpy.pi*Qy)
M00 = c_dphi_x + alphax * s_dphi_x
M01 = betax * s_dphi_x
M10 = -(1. + alphax**2) / betax * s_dphi_x
M11 = c_dphi_x - alphax * s_dphi_x
M04 = (1 - M00) * dispx - M01 * dispxp
M14 = -M10 * dispx + (1 - M11) * dispxp
M22 = c_dphi_y + alphay * s_dphi_y
M23 = betay * s_dphi_y
M32 = -(1. + alphay**2) / betay * s_dphi_y
M33 = c_dphi_y - alphay * s_dphi_y
M24 = (1 - M22) * dispy - M23 * dispyp
M34 = -M32 * dispy + (1 - M33) * dispyp
M44 = 1.
M45 = 0.
M54 = alpha*circumference
M55 = 1
Mat66 = numpy.array([[M00, M01, 0., 0., M04, 0.],
[M10, M11, 0., 0., M14, 0.],
[0., 0., M22, M23, M24, 0.],
[0., 0., M32, M33, M34, 0.],
[0., 0., 0., 0., M44, M45],
[0., 0., 0., 0., M54, M55]], order='F')
# generate the linear tracking element, we set a length
# which is needed to give the lattice object the correct length
# (although it is not used for anything else)
lin_elem = M66('Linear', m66=Mat66, Length=circumference)
# Generate the simple radiation element
simplerad = SimpleRadiation('SR', taux=taux, tauy=tauy,
tauz=tauz, U0=U0, dispx=dispx,
dispy=dispy, dispxp=dispxp,
dispyp=dispyp)
# Generate the simple quantum diffusion element
quantdiff = SimpleQuantDiff('SQD', betax=betax, betay=betay,
emitx=emitx, emity=emity,
espread=espread, taux=taux,
tauy=tauy, tauz=tauz)
# Generate the detuning element
nonlin_elem = Element('NonLinear', PassMethod='DeltaQPass',
Betax=betax, Betay=betay,
Alphax=alphax, Alphay=alphay,
Qpx=Qpx, Qpy=Qpy,
A1=A1, A2=A2, A3=A3)
# Assemble all elements into the lattice object
ring = Lattice(all_cavities + [lin_elem, nonlin_elem, simplerad, quantdiff],
name=name, energy=energy, particle=particle, periodicity=1)
return ring
