Traveling Wave Cavity¶

A traveling wave needs to be described by four fieldmaps: entrance two body exit

http://accelconf.web.cern.ch/accelconf/p79/PDF/PAC1979_3701.PDF

0.052464 0 0 105 1.42 25500000.0 2856000000.0 119.0 4 0.15 0.0 0.0 0.0 0.0 0.0 0.0 /!name:entrance
2.937928 0 0 105 1.472464 29430178.7820912 2856000000.0 149.0 5 0.15 0.0 0.0 0.0 0.0 0.0 0.0 /!name:body_1
2.937928 0 0 105 1.472464 29430178.7820912 2856000000.0 209.0 6 0.15 0.0 0.0 0.0 0.0 0.0 0.0 /!name:body_2
0.05246 0 0 105 4.410392 25500000.0 2856000000.0 119.0 7 0.15 0.0 0.0 0.0 0.0 0.0 0.0 /!name:exit

The following 4 lines define a 3-cell s-band traveling wave structure using the supperposition of two standing wave strutures. G. A. Loew et al., SLAC-PUB-2295, 1979.

• the phase of line 2 is the phase of line 1 + 30 degrees;
• the phase of line 3 is the phase of line 1 + 90 degrees.
• the phase of line 4 is the same as the line 1;
• the field scale of line 2 is the scale of the line 1/sin(beta d)
• the field scale of line 3 is the scale of the line 1/sin(beta d)
• the scale of line 4 is the same as the line 1;

In [1]:

# Useful for debugging
%load_ext autoreload
%autoreload 2

import numpy as np
import os

import matplotlib.pyplot as plt

%matplotlib inline

# Useful for debugging %load_ext autoreload %autoreload 2 import numpy as np import os import matplotlib.pyplot as plt %matplotlib inline

In [2]:

frf = 2856000000.0
c = 299792458.0
pi = np.pi
k = 2 * pi * frf / c
d = 3.5e-2  # periodic length
(
    np.sin(k * d),
    25905612.0 / 29913224.7,
)  # = 0.86571945106805 #roughly equals 25905612.0/29913224.7 as above

frf = 2856000000.0 c = 299792458.0 pi = np.pi k = 2 * pi * frf / c d = 3.5e-2 # periodic length ( np.sin(k * d), 25905612.0 / 29913224.7, ) # = 0.86571945106805 #roughly equals 25905612.0/29913224.7 as above

Out[2]:

(np.float64(0.86571945106805), 0.8660253870924187)

In [3]:

frf / c

frf / c

Out[3]:

9.526590558859223

In [4]:

from impact import Impact, fieldmaps

from impact import Impact, fieldmaps

In [5]:

ifile = "../templates/traveling_wave_cavity/ImpactT.in"
os.path.exists(ifile)

ifile = "../templates/traveling_wave_cavity/ImpactT.in" os.path.exists(ifile)

Out[5]:

True

In [6]:

I = Impact(ifile)

I = Impact(ifile)

In [7]:

# I.run()

# I.run()

Fieldmaps¶

In [8]:

I.input["fieldmaps"]
fmap4 = I.input["fieldmaps"]["rfdata4"]["field"]["Ez"]
fmap5 = I.input["fieldmaps"]["rfdata5"]["field"]["Ez"]
fmap6 = I.input["fieldmaps"]["rfdata6"]["field"]["Ez"]
fmap7 = I.input["fieldmaps"]["rfdata7"]["field"]["Ez"]
# fmap4 = fieldmaps.process_fieldmap_solrf(rdfa['field']['Ez']ta4['data'])['Ez']
# fmap5 = fieldmaps.process_fieldmap_solrf(rdfata5['data'])['Ez']
# fmap6 = fieldmaps.process_fieldmap_solrf(rdfata6['data'])['Ez']
# fmap7 = fieldmaps.process_fieldmap_solrf(rdfata7['data'])['Ez']

I.input["fieldmaps"] fmap4 = I.input["fieldmaps"]["rfdata4"]["field"]["Ez"] fmap5 = I.input["fieldmaps"]["rfdata5"]["field"]["Ez"] fmap6 = I.input["fieldmaps"]["rfdata6"]["field"]["Ez"] fmap7 = I.input["fieldmaps"]["rfdata7"]["field"]["Ez"] # fmap4 = fieldmaps.process_fieldmap_solrf(rdfa['field']['Ez']ta4['data'])['Ez'] # fmap5 = fieldmaps.process_fieldmap_solrf(rdfata5['data'])['Ez'] # fmap6 = fieldmaps.process_fieldmap_solrf(rdfata6['data'])['Ez'] # fmap7 = fieldmaps.process_fieldmap_solrf(rdfata7['data'])['Ez']

In [9]:

fieldmaps.fieldmap_reconstruction_solrf(fmap4, 0)

fieldmaps.fieldmap_reconstruction_solrf(fmap4, 0)

Out[9]:

np.float64(0.00029705336845264885)

In [10]:

fmap4

fmap4

Out[10]:

{'z0': np.float64(-0.052464),
 'z1': np.float64(0.052464),
 'L': np.float64(0.104928),
 'fourier_coefficients': array([ 6.70002854e-01, -4.88198923e-01,  1.13480302e-08,  1.84595508e-01,
        -7.71467877e-09, -2.13348183e-02,  6.02607452e-10, -1.74781481e-02,
         4.51769540e-09,  1.09000464e-02, -5.96395860e-10, -2.45640689e-03,
         5.31099067e-08, -8.37267976e-04,  7.96730829e-08,  6.58132017e-04,
         2.30345527e-08, -2.85586070e-04, -1.99486350e-08, -6.43828139e-05,
         1.41973546e-08, -8.32668961e-07,  5.47140406e-08, -5.38330720e-05,
         5.84708220e-08, -2.85487322e-05, -3.37187380e-08, -2.81781237e-05,
         2.19574641e-08, -2.54874681e-05, -8.91928108e-08, -1.42715353e-05,
         6.80653280e-08, -2.43108787e-05, -9.59187448e-09, -1.48944953e-05,
        -3.21672254e-09, -1.21690943e-05, -2.00760664e-08])}

In [11]:

fmap = fmap6
zlist = np.linspace(fmap["z0"], fmap["z1"], 1000)
fieldlist = [fieldmaps.fieldmap_reconstruction_solrf(fmap, z) for z in zlist]
fig, ax = plt.subplots(figsize=(20, 5))
ax.plot(zlist, fieldlist)

fmap = fmap6 zlist = np.linspace(fmap["z0"], fmap["z1"], 1000) fieldlist = [fieldmaps.fieldmap_reconstruction_solrf(fmap, z) for z in zlist] fig, ax = plt.subplots(figsize=(20, 5)) ax.plot(zlist, fieldlist)

Out[11]:

[<matplotlib.lines.Line2D at 0x7f41272c4710>]

In [12]:

fieldlist5 = np.array(
    [fieldmaps.fieldmap_reconstruction_solrf(fmap5, z) for z in zlist]
)
fieldlist6 = np.array(
    [fieldmaps.fieldmap_reconstruction_solrf(fmap6, z) for z in zlist]
)

fieldlist5 = np.array( [fieldmaps.fieldmap_reconstruction_solrf(fmap5, z) for z in zlist] ) fieldlist6 = np.array( [fieldmaps.fieldmap_reconstruction_solrf(fmap6, z) for z in zlist] )

In [13]:

l = c / frf
l

l = c / frf l

Out[13]:

0.10496934803921569

In [14]:

fig, ax = plt.subplots(figsize=(20, 5))

wt = 2 * np.pi / 360 * 0
plt.ylim(-1, 1)
plt.xlim(0, 0.5)
ax.plot(zlist + l * 2 / 3, fieldlist5 * np.cos(wt))
ax.plot(zlist, fieldlist6 * np.cos(wt))

fig, ax = plt.subplots(figsize=(20, 5)) wt = 2 * np.pi / 360 * 0 plt.ylim(-1, 1) plt.xlim(0, 0.5) ax.plot(zlist + l * 2 / 3, fieldlist5 * np.cos(wt)) ax.plot(zlist, fieldlist6 * np.cos(wt))

Out[14]:

[<matplotlib.lines.Line2D at 0x7f411e86c9b0>]

In [15]:

fig, ax = plt.subplots(figsize=(20, 5))

wt = 2 * np.pi / 360 * 90
plt.ylim(-1, 1)
ax.plot(zlist, fieldlist5 * np.cos(wt) + fieldlist6 * np.cos(wt + 2 * np.pi * 60 / 360))

fig, ax = plt.subplots(figsize=(20, 5)) wt = 2 * np.pi / 360 * 90 plt.ylim(-1, 1) ax.plot(zlist, fieldlist5 * np.cos(wt) + fieldlist6 * np.cos(wt + 2 * np.pi * 60 / 360))

Out[15]:

[<matplotlib.lines.Line2D at 0x7f411e8c16a0>]

In [16]:

0.0586460 + 0.3371281 + 1.1518479 + 1.1515630 + 0.3351400 + 0.0609190

0.0586460 + 0.3371281 + 1.1518479 + 1.1515630 + 0.3351400 + 0.0609190

Out[16]:

3.095244

In [17]:

0.0586460 + 0.3371281 + 1.1518479

0.0586460 + 0.3371281 + 1.1518479

Out[17]:

1.5476219999999998

In [18]:

1.1515630 + 0.3351400 + 0.0609190

1.1515630 + 0.3351400 + 0.0609190

Out[18]:

1.5476219999999998

ControlGroups¶

In [19]:

from impact import ControlGroup

from impact import ControlGroup

In [20]:

# Add a ControlGroup that can change the relative phase

I2 = I.copy()

CAV = ControlGroup(
    ele_names=["solrf_entrance", "solrf_body_1", "solrf_body_2", "solrf_exit"],
    var_name="dtheta0_deg",
    attributes="theta0_deg",
)
CAV.link(I2.ele)
[ele["theta0_deg"] for ele in CAV.eles]

# Add a ControlGroup that can change the relative phase I2 = I.copy() CAV = ControlGroup( ele_names=["solrf_entrance", "solrf_body_1", "solrf_body_2", "solrf_exit"], var_name="dtheta0_deg", attributes="theta0_deg", ) CAV.link(I2.ele) [ele["theta0_deg"] for ele in CAV.eles]

Out[20]:

[119.0, 149.0, 209.0, 119.0]

In [21]:

CAV["dtheta0_deg"] = 0
[ele["theta0_deg"] for ele in CAV.eles]

CAV["dtheta0_deg"] = 0 [ele["theta0_deg"] for ele in CAV.eles]

Out[21]:

[119.0, 149.0, 209.0, 119.0]

In [22]:

CAV_scale = ControlGroup(
    ele_names=["solrf_entrance", "solrf_body_1", "solrf_body_2", "solrf_exit"],
    var_name="rf_field_scale",
    factors=[0.86571945106805, 1, 1, 0.86571945106805],  # sin(k*d) with d = 3.5e-2 m
    absolute=True,
)
CAV_scale.link(I2.ele)

CAV_scale = ControlGroup( ele_names=["solrf_entrance", "solrf_body_1", "solrf_body_2", "solrf_exit"], var_name="rf_field_scale", factors=[0.86571945106805, 1, 1, 0.86571945106805], # sin(k*d) with d = 3.5e-2 m absolute=True, ) CAV_scale.link(I2.ele)

In [23]:

CAV_scale["rf_field_scale"] = 29e6
[ele["rf_field_scale"] for ele in CAV_scale.eles]

CAV_scale["rf_field_scale"] = 29e6 [ele["rf_field_scale"] for ele in CAV_scale.eles]

Out[23]:

[25105864.08097345, 29000000.0, 29000000.0, 25105864.08097345]

Autophase and scale¶

In [24]:

#  Changes in phases
I.add_group(
    "L0A",
    ele_names=["solrf_entrance", "solrf_body_1", "solrf_body_2", "solrf_exit"],
    var_name="theta0_deg",
    attributes="theta0_deg",
)


# Overall scaling, respecting the special factors.
I.add_group(
    "L0A_scale",
    ele_names=["solrf_entrance", "solrf_body_1", "solrf_body_2", "solrf_exit"],
    var_name="rf_field_scale",
    factors=[0.86571945106805, 1, 1, 0.86571945106805],  # sin(k*d) with d = 3.5e-2 m
    absolute=True,
)

# Changes in phases I.add_group( "L0A", ele_names=["solrf_entrance", "solrf_body_1", "solrf_body_2", "solrf_exit"], var_name="theta0_deg", attributes="theta0_deg", ) # Overall scaling, respecting the special factors. I.add_group( "L0A_scale", ele_names=["solrf_entrance", "solrf_body_1", "solrf_body_2", "solrf_exit"], var_name="rf_field_scale", factors=[0.86571945106805, 1, 1, 0.86571945106805], # sin(k*d) with d = 3.5e-2 m absolute=True, )

Out[24]:

ControlGroup(**{"ele_names": ["solrf_entrance", "solrf_body_1", "solrf_body_2", "solrf_exit"], "var_name": "rf_field_scale", "attributes": ["rf_field_scale", "rf_field_scale", "rf_field_scale", "rf_field_scale"], "factors": [0.86571945106805, 1.0, 1.0, 0.86571945106805], "reference_values": [25500000.0, 29430178.7820912, 29430178.7820912, 25500000.0], "absolute": true, "value": 0.0, "name": "L0A_scale"})

In [25]:

from impact.autophase import autophase_and_scale

from pmd_beamphysics import single_particle

# Start particles at 1.4 m, just in front of the cavity
P0 = single_particle(pz=6e6, z=1.4)

from impact.autophase import autophase_and_scale from pmd_beamphysics import single_particle # Start particles at 1.4 m, just in front of the cavity P0 = single_particle(pz=6e6, z=1.4)

In [26]:

autophase_and_scale(
    I,
    phase_ele_name="L0A",
    scale_ele_name="L0A_scale",
    target=64e6,
    scale_range=(10e6, 100e6),
    initial_particles=P0,
    verbose=True,
)

autophase_and_scale( I, phase_ele_name="L0A", scale_ele_name="L0A_scale", target=64e6, scale_range=(10e6, 100e6), initial_particles=P0, verbose=True, )

Copied initial Impact object. 
Phasing L0A by changing theta0_deg
Scaling L0A_scale by changing rf_field_scale
Bounds: 1.42, 4.462852 m
Tracking initial particles to s = 1.42
Initial particle:  1.42001364304 6021791.459371396
Disabling solrf_1
Disabling solrf_2
Default brent2 algorithm

Phase: 180, Scale: 10000000.0, 24.856464772583482 MeV

Phase: 180, Scale: 10000000.0, 24.856464772583482 MeV

Phase: 42.49224000000004, Scale: 10000000.0, 8.578906397705104 MeV

Phase: 42.49223094384001, Scale: 10000000.0, 8.57890756562477 MeV

Phase: 42.49223999999998, Scale: 10000000.0, 8.578906397705104 MeV

Phase: 222.4922385207506, Scale: 10000000.0, 16.496521287751712 MeV

Phase: 127.47671094383999, Scale: 10000000.0, 21.05105889847044 MeV

Phase: 166.52483783762918, Scale: 10000000.0, 25.312859819887922 MeV

Phase: 167.04288955059457, Scale: 10000000.0, 25.315101189536623 MeV

Phase: 167.517704554632, Scale: 10000000.0, 25.31578171810014 MeV

Phase: 167.68522225919662, Scale: 10000000.0, 25.315707803718432 MeV

Phase: 167.35018685006736, Scale: 10000000.0, 25.315691786975584 MeV
Step 1 phasing found: 167.517704554632

Phase: 167.517704554632, Scale: 10000000.0, 25.31578171810014 MeV

Phase: 167.517704554632, Scale: 100000000.0, 198.2193693243856 MeV

Phase: 167.517704554632, Scale: 30135959.545841277, 64.08457393061273 MeV

Phase: 167.517704554632, Scale: 30092033.04856698, 64.0001401656686 MeV

Phase: 167.517704554632, Scale: 30076987.032042693, 63.97121923669888 MeV
Step 2  scale found: 30092033.04856698

Phase: 166.517704554632, Scale: 30092033.04856698, 63.930448123915845 MeV

Phase: 168.517704554632, Scale: 30092033.04856698, 64.05236338810258 MeV

Phase: 171.75377255463198, Scale: 30092033.04856698, 64.10102785908452 MeV

Phase: 170.99311718390493, Scale: 30092033.04856698, 64.10616594870606 MeV

Phase: 170.04759372355207, Scale: 30092033.04856698, 64.09833350578708 MeV

Phase: 170.63195936984778, Scale: 30092033.04856698, 64.10503293842714 MeV

Phase: 170.99064296460674, Scale: 30092033.04856698, 64.10616600798076 MeV

Phase: 170.99047197395376, Scale: 30092033.04856698, 64.10616600798076 MeV

Phase: 170.9903009834718, Scale: 30092033.04856698, 64.10616600798076 MeV

Phase: 170.8534266706823, Scale: 30092033.04856698, 64.1060003428681 MeV

Phase: 170.93801964971286, Scale: 30092033.04856698, 64.10614171148696 MeV

Phase: 170.97033129154124, Scale: 30092033.04856698, 64.10616241521876 MeV

Phase: 170.98267324012386, Scale: 30092033.04856698, 64.1061654653107 MeV

Phase: 170.98738744485615, Scale: 30092033.04856698, 64.10616592162367 MeV

Phase: 170.98918811078093, Scale: 30092033.04856698, 64.1061659926511 MeV

Phase: 170.98987590394157, Scale: 30092033.04856698, 64.10616600440385 MeV

Phase: 170.99012999316082, Scale: 30092033.04856698, 64.10616600695879 MeV
Step 3 phase found:  170.9903009834718

Phase: 170.9903009834718, Scale: 10000000.0, 25.28060814017475 MeV

Phase: 170.9903009834718, Scale: 100000000.0, 198.94886639590493 MeV

Phase: 170.9903009834718, Scale: 30065527.819441315, 64.05500111759288 MeV

Phase: 170.9903009834718, Scale: 30037065.05392999, 64.00005737067866 MeV

Phase: 170.9903009834718, Scale: 30037035.33397374, 63.999999999932065 MeV
Step 4 scale found:  30037035.33397374
Set Phase: 170.9903009834718, Scale: 30037035.33397374

Out[26]:

(np.float64(170.9903009834718), 30037035.33397374)

In [27]:

PF = I.track(P0, 4.5)
PF["mean_energy"]

PF = I.track(P0, 4.5) PF["mean_energy"]

Out[27]:

np.float64(63999921.25861558)

Track distgen particles¶

In [28]:

from distgen import Generator

YAML = """
n_particle: 20000
random_type: hammersley
species: electron
start:
  tstart:
    units: sec
    value: 0
  type: time
total_charge:
  units: pC
  value: 250.0
r_dist:
  sigma_xy:
    units: mm
    value: 0.01
  type: radial_gaussian
z_dist:
  avg_z:
    units: m
    value: 1.4
  sigma_z:
    units: mm
    value: 0.01
  type: gaussian
  

transforms:
  setPz:
    type: set_avg pz
    avg_pz: 
      value: 6
      units: MeV/c
  
"""
G = Generator(YAML)
G.run()
DP = G.particles
DP.plot("z", "pz")

from distgen import Generator YAML = """ n_particle: 20000 random_type: hammersley species: electron start: tstart: units: sec value: 0 type: time total_charge: units: pC value: 250.0 r_dist: sigma_xy: units: mm value: 0.01 type: radial_gaussian z_dist: avg_z: units: m value: 1.4 sigma_z: units: mm value: 0.01 type: gaussian transforms: setPz: type: set_avg pz avg_pz: value: 6 units: MeV/c """ G = Generator(YAML) G.run() DP = G.particles DP.plot("z", "pz")

In [29]:

DP["min_z"]

DP["min_z"]

Out[29]:

np.float64(1.3999585342792105)

In [30]:

I.header["Bcurr"] = 0  # SC off
I.header["Dt"] = 1e-11
PF = I.track(DP, 5)

I.header["Bcurr"] = 0 # SC off I.header["Dt"] = 1e-11 PF = I.track(DP, 5)

In [31]:

PI = I.particles["initial_particles"]
PI.plot("z", "x")

PI = I.particles["initial_particles"] PI.plot("z", "x")

In [32]:

PF.plot("delta_z", "delta_pz")

PF.plot("delta_z", "delta_pz")

In [33]:

# Compare these.
key1 = "mean_z"
key2 = "mean_kinetic_energy"
units1 = str(I.units(key1))
units2 = str(I.units(key2))
plt.xlabel(key1 + f" ({units1})")
plt.ylabel(key2 + f" ({units2})")
plt.plot(I.stat(key1), I.stat(key2))
plt.scatter(
    [I.particles[name][key1] for name in I.particles],
    [I.particles[name][key2] for name in I.particles],
    color="red",
)

# Compare these. key1 = "mean_z" key2 = "mean_kinetic_energy" units1 = str(I.units(key1)) units2 = str(I.units(key2)) plt.xlabel(key1 + f" ({units1})") plt.ylabel(key2 + f" ({units2})") plt.plot(I.stat(key1), I.stat(key2)) plt.scatter( [I.particles[name][key1] for name in I.particles], [I.particles[name][key2] for name in I.particles], color="red", )

Out[33]:

<matplotlib.collections.PathCollection at 0x7f4126fc2fc0>