Correction to Zeuthen chicane input (#590)

* Examples for 3D space charge benchmarking

- Modified the initial beam size in the IOTA lens benchmark example.
- Added 2 benchmarks of 3D space charge for initial testing.
- Add documentation for 2 benchmarks with space charge.
- Add a benchmark example with space charge and periodic s-dependent focusing.
- Added an s-dependent example using a Kurth beam without space charge.
- Modified tolerance for IOTA lens benchmark example.
  Reduced tolerance to account for smaller initial beam size and
  improved preservation of invariants of motion.
- Modified tolerances of space charge examples to allow CI tests to
  pass when space charge is not active.

- Modified tolerance for space charge examples.
  These should fail unless space charge is turned on.

* Update input_kurth_10nC.in

Selected numerical values for amr.n_cell, lattice.nslice, and geometry.prob_relative.

* Add README documentation for examples/distgen

* Correct C++ input file.

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Delete examples/kurth/input_kurth_10nC.in

Not part of this pr

* Modify Python and MAD-X input

* Delete examples/distgen/README.rst

Not part of this PR.

* Update run_chicane.py

Update lb comment.

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

examples/chicane/chicane.madx

@@ -8,11 +8,11 @@ D3: drift, L=2.0;
 ! theta=0.50037/10.35;
 ! inv_rho=1.0/10.35
 ! TODO put `angle=theta` for SBENDs and `e1=theta` for DIPEDGEs with their right sign
-SB1: sbend, L=0.50037, angle=-0.04834492753623188, e1=0.000, e2=0.000, k1=0.00;
-SB2: sbend, L=0.50037, angle=0.04834492753623188, e1=0.000, e2=0.000, k1=0.00;
+SB1: sbend, L=0.500194828041958, angle=-0.04834492753623188, e1=0.000, e2=0.000, k1=0.00;
+SB2: sbend, L=0.500194828041958, angle=0.04834492753623188, e1=0.000, e2=0.000, k1=0.00;
 ! dipole edge elements
-DIPE1: dipedge, H=-0.0966183574879227, e1=-0.048345620280243, fint=0.000, hgap=0.000, tilt=0.00;
-DIPE2: dipedge, H=0.0966183574879227, e1=0.048345620280243, fint=0.000, hgap=0.000, tilt=0.00;
+DIPE1: dipedge, H=-0.096653578905433, e1=-0.048345620280243, fint=0.000, hgap=0.000, tilt=0.00;
+DIPE2: dipedge, H=0.096653578905433, e1=0.048345620280243, fint=0.000, hgap=0.000, tilt=0.00;
 
 CHICANE:     Line=(M1,SB1,DIPE1,D1,DIPE2,SB2,D2,SB2,DIPE2,D1,DIPE1,SB1,D3,M1);
 USE, SEQUENCE = CHICANE;

examples/chicane/input_chicane.in

@@ -26,15 +26,15 @@ lattice.elements = monitor sbend1 dipedge1 drift1 dipedge2 sbend2 drift2      \
 lattice.nslice = 25
 
 sbend1.type = sbend
-sbend1.ds = 0.50037       # projected length 0.5 m, angle 2.77 deg
-sbend1.rc = -10.35
+sbend1.ds = 0.500194828041958       # projected length 0.5 m, angle 2.77 deg
+sbend1.rc = -10.3462283686195526
 
 drift1.type = drift
 drift1.ds = 5.0058489435  # projected length 5 m
 
 sbend2.type = sbend
-sbend2.ds = 0.50037       # projected length 0.5 m, angle 2.77 deg
-sbend2.rc = 10.35
+sbend2.ds = 0.500194828041958       # projected length 0.5 m, angle 2.77 deg
+sbend2.rc = 10.3462283686195526
 
 drift2.type = drift
 drift2.ds = 1.0
@@ -44,13 +44,13 @@ drift3.ds = 2.0
 
 dipedge1.type = dipedge   # dipole edge focusing
 dipedge1.psi = -0.048345620280243
-dipedge1.rc = -10.35
+dipedge1.rc = -10.3462283686195526
 dipedge1.g = 0.0
 dipedge1.K2 = 0.0
 
 dipedge2.type = dipedge
 dipedge2.psi = 0.048345620280243
-dipedge2.rc = 10.35
+dipedge2.rc = 10.3462283686195526
 dipedge2.g = 0.0
 dipedge2.K2 = 0.0
 

examples/chicane/run_chicane.py

@@ -48,17 +48,18 @@
 
 # design the accelerator lattice
 ns = 25  # number of slices per ds in the element
-rc = 10.35  # bend radius (meters)
+rc = 10.3462283686195526  # bend radius (meters)
 psi = 0.048345620280243  # pole face rotation angle (radians)
+lb = 0.500194828041958  # bend arc length (meters)
 
 # Drift elements
 dr1 = elements.Drift(ds=5.0058489435, nslice=ns)
 dr2 = elements.Drift(ds=1.0, nslice=ns)
 dr3 = elements.Drift(ds=2.0, nslice=ns)
 
 # Bend elements
-sbend1 = elements.Sbend(ds=0.50037, rc=-rc, nslice=ns)
-sbend2 = elements.Sbend(ds=0.50037, rc=rc, nslice=ns)
+sbend1 = elements.Sbend(ds=lb, rc=-rc, nslice=ns)
+sbend2 = elements.Sbend(ds=lb, rc=rc, nslice=ns)
 
 # Dipole Edge Focusing elements
 dipedge1 = elements.DipEdge(psi=-psi, rc=-rc, g=0.0, K2=0.0)