From 40492f75aa4af43be3dead68d285fadb50907d0a Mon Sep 17 00:00:00 2001
From: Alexis Gamelin <alexis.gamelin@synchrotron-soleil.fr>
Date: Tue, 11 Feb 2025 11:37:06 +0100
Subject: [PATCH] Add transverse_space_charge_tune_shift utility function
---
mbtrack2/instability/__init__.py | 2 +
mbtrack2/instability/space_charge.py | 83 ++++++++++++++++++++++++++++
2 files changed, 85 insertions(+)
create mode 100644 mbtrack2/instability/space_charge.py
diff --git a/mbtrack2/instability/__init__.py b/mbtrack2/instability/__init__.py
index f7a1516..6d59c92 100644
--- a/mbtrack2/instability/__init__.py
+++ b/mbtrack2/instability/__init__.py
@@ -14,3 +14,5 @@ from mbtrack2.instability.ions import (
ion_frequency,
plot_critical_mass,
)
+from mbtrack2.instability.space_charge import (
+ transverse_space_charge_tune_shift, )
diff --git a/mbtrack2/instability/space_charge.py b/mbtrack2/instability/space_charge.py
new file mode 100644
index 0000000..bd763e3
--- /dev/null
+++ b/mbtrack2/instability/space_charge.py
@@ -0,0 +1,83 @@
+# -*- coding: utf-8 -*-
+"""
+General calculations about space charge such as tune shift.
+"""
+
+import numpy as np
+from scipy.constants import c, epsilon_0, pi
+
+
+def transverse_space_charge_tune_shift(ring, bunch_current, **kwargs):
+ """
+ Return the (maximum) transverse space charge tune shift for a Gaussian
+ bunch in the linear approximation, see Eq.(1) of [1].
+
+ Parameters
+ ----------
+ ring : Synchrotron object
+ Ring parameters.
+ bunch_current : float
+ Bunch current in [A].
+ sigma_s : float, optional
+ RMS bunch length in [s].
+ Default is ring.sigma_0.
+ emit_x : float, optional
+ Horizontal emittance in [m.rad].
+ Default is ring.emit[0].
+ emit_y : float, optional
+ Vertical emittance in [m.rad].
+ Default is ring.emit[1].
+ use_lattice : bool, optional
+ If True, use beta fonctions along the lattice.
+ If False, local values of beta fonctions are used.
+ Default is ring.optics.use_local_values.
+ sigma_delta : float, optional
+ Relative energy spread.
+ Default is ring.sigma_delta.
+ gamma : float, optional
+ Relativistic Lorentz gamma.
+ Default is ring.gamma.
+
+ Returns
+ -------
+ tune_shift : array of shape (2,)
+ Horizontal and vertical space charge tune shift.
+
+ Reference
+ ---------
+ [1] : Antipov, S. A., Gubaidulin, V., Agapov, I., Garcia, E. C., &
+ Gamelin, A. (2024). Space Charge and Future Light Sources.
+ arXiv preprint arXiv:2409.08637.
+
+ """
+ sigma_s = kwargs.get('sigma_s', ring.sigma_0)
+ emit_x = kwargs.get('emit_x', ring.emit[0])
+ emit_y = kwargs.get('emit_y', ring.emit[1])
+ use_lattice = kwargs.get('use_lattice', not ring.optics.use_local_values)
+ sigma_delta = kwargs.get('sigma_delta', ring.sigma_delta)
+ gamma = kwargs.get('gamma', ring.gamma)
+
+ q = np.abs(ring.particle.charge)
+ m = ring.particle.mass
+ r_0 = 1 / (4*pi*epsilon_0) * q**2 / (m * c**2)
+ N = bunch_current / ring.f0 / q
+ sigma_z = sigma_s * c
+
+ if use_lattice:
+ s = np.linspace(0, ring.L, 1000)
+ beta = ring.optics.beta(s)
+ sig_x = (emit_x * beta[0] +
+ ring.optics.dispersion(s)[0]**2 * sigma_delta**2)**0.5
+ sig_y = (emit_y * beta[1] +
+ ring.optics.dispersion(s)[2]**2 * sigma_delta**2)**0.5
+ sig_xy = np.array([sig_x, sig_y])
+ return -r_0 * N / ((2 * pi)**1.5 * gamma**3 * sigma_z) * np.trapz(
+ beta / (sig_xy * (sig_y+sig_x)), s)
+ else:
+ beta = ring.optics.local_beta
+ sig_x = np.sqrt(beta[0] * emit_x)
+ sig_y = np.sqrt(beta[1] * emit_y)
+ sig_xy = np.array([sig_x, sig_y])
+ return -r_0 * N * ring.L / (
+ (2 * pi)**1.5 * gamma**3 * sigma_z) * beta / (sig_xy *
+ (sig_y+sig_x))
--
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