From b965100e36d296124880492d902251f6988a3e9e Mon Sep 17 00:00:00 2001
From: Gamelin Alexis <alexis.gamelin@synchrotron-soleil.fr>
Date: Thu, 3 Mar 2022 10:13:32 +0100
Subject: [PATCH] Add non-linear model to FBII rise time calculation
Correct typo in ion_frequency
---
collective_effects/ions.py | 43 ++++++++++++++++++++++++++++----------
1 file changed, 32 insertions(+), 11 deletions(-)
diff --git a/collective_effects/ions.py b/collective_effects/ions.py
index 66be6a0..bac8d8e 100644
--- a/collective_effects/ions.py
+++ b/collective_effects/ions.py
@@ -56,7 +56,7 @@ def ion_cross_section(ring, ion):
return sigma
-def ion_frequency(N, Lesp, sigmax, sigmay, ion="CO", dim="y", express="coupling"):
+def ion_frequency(N, Lsep, sigmax, sigmay, ion="CO", dim="y", express="coupling"):
"""
Compute the ion oscillation frequnecy.
@@ -64,7 +64,7 @@ def ion_frequency(N, Lesp, sigmax, sigmay, ion="CO", dim="y", express="coupling"
----------
N : float
Number of electrons per bunch.
- Lesp : float
+ Lsep : float
Bunch spacing in [m].
sigmax : float or array
Horizontal beam size in [m].
@@ -118,22 +118,32 @@ def ion_frequency(N, Lesp, sigmax, sigmay, ion="CO", dim="y", express="coupling"
elif express == "no_coupling":
k = 1
- f = c * np.sqrt( 2 * rp * N / ( A * k * Lesp * sigmay * (sigmax + sigmay) ) ) / (2*pi)
+ f = c * np.sqrt( 2 * rp * N / ( A * k * Lsep * sigmay * (sigmax + sigmay) ) ) / (2*pi)
return f
def fast_beam_ion(ring, Nb, nb, Lsep, sigmax, sigmay, P, T, beta,
- decoherence=True, delta_omega = 0, ion="CO", dim="y"):
+ model="linear", delta_omega = 0, ion="CO", dim="y"):
"""
Compute fast beam ion instability rise time [1].
- Warning ! If decoherence=False, the rise time is not an e-folding time
- (i.e. y ~ exp(t/tau)) but an assymptotic grow time
- (i.e. y ~ exp(sqrt(t/tau))) see [1][2].
+ Warning !
+ If model="linear", the rise time is an assymptotic grow time
+ (i.e. y ~ exp(sqrt(t/tau))) [1].
+ If model="decoherence", the rise time is an e-folding time
+ (i.e. y ~ exp(t/tau)) [2].
+ If model="non-linear", the rise time is a linear growth time
+ (i.e. y ~ t/tau) [3].
+
+ The linear model assumes that [1]:
+ x,y << sigmax,sigmay
The decoherence model assumes that [2]:
Lsep << c / (2 * pi * ion_frequency)
- Lsep << c / (2 * pi * betatron_frequency)
+ Lsep << c / (2 * pi * betatron_frequency)
+
+ The non-linear model assumes that [3]:
+ x,y >> sigmax,sigmay
Parameters
----------
@@ -154,8 +164,10 @@ def fast_beam_ion(ring, Nb, nb, Lsep, sigmax, sigmay, P, T, beta,
Tempertature in [K].
beta : float
Average betatron function around the ring in [m].
- decoherence : bool, optional
- If True, decoherence is taken into account using [2].
+ model : str, optional
+ If "linear", use [1].
+ If "decoherence", use [2].
+ If "non-linear", use [3].
delta_omega : float, optional
RMS variation of the ion oscillation angular frequnecy around the ring
in [Hz].
@@ -175,6 +187,8 @@ def fast_beam_ion(ring, Nb, nb, Lsep, sigmax, sigmay, P, T, beta,
linear theory and simulations", Physical Review E 52 (1995).
[2] : G. V. Stupakov, T. O. Raubenheimer, and F. Zimmermann, "Fast beam-ion
instability. II. effect of ion decoherence", Physical Review E 52 (1995).
+ [3] : Chao, A. W., & Mess, K. H. (Eds.). (2013). Handbook of accelerator
+ physics and engineering. World scientific. 3rd Printing. p417.
"""
if dim == "y":
@@ -198,8 +212,15 @@ def fast_beam_ion(ring, Nb, nb, Lsep, sigmax, sigmay, P, T, beta,
tau = den/num
- if decoherence is True:
+ if model == "decoherence":
tau = tau * 2 * np.sqrt(2) * nb * Lsep * delta_omega / c
+ elif model == "non-linear":
+ fi = ion_frequency(Nb, Lsep, sigmax, sigmay, ion, dim)
+ tau = tau * 2 * pi * fi * ring.T1 * nb**(3/2)
+ elif model == "linear":
+ pass
+ else:
+ raise ValueError("model unknown")
return tau
--
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