Add non-linear model to FBII rise time calculation

Correct typo in ion_frequency

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