USPAS_AP_ComputerLab/longitudinal.py at master · yuehao/USPAS_AP_ComputerLab · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158

import numpy as np
import math


def longitudinal_evolve(turns, phi_list_ini, dE_list_ini, sin_phi_s=0, E0_ini=100e9, mass=938e6, e_volt=5e6, alphac=0.002, harm=360.0, update_eta=True, energy_change=False, gamma_jump=[0, 0, 0.0], phase_jump=[-1,0.0]):
    '''
    The function of longitudinal map.

    Parameters:
    turns: number of turns used in the simulation
    phi_list_ini: list of values for initial phase
    dE_list_ini: list of values for initial energy deviation
    sin_phi_s: sine value of the phi_s, default 0
    E0_ini: Initial energy at tune zero, default 100e9 eV
    mass: Rest energy of the particle, default 938e6 eV
    e_volt: The voltage of the cavity including transit time factor, default 5e6 V
    alphac: \alpha_c of the ring, default 0.002
    harm: harmonic of the ring, default 1
    update_eta:  Always update phase slip factor due to energy change, default True
    energy_change: The beam get acceleration/ deceleration due to non zero sin_phi_s, default False

    return: the tuple of stacked numpy arrays: (phi, de, delta)
    '''
    E0 = E0_ini
    p0_ini=np.sqrt(E0_ini*E0_ini-mass*mass)
    p0=p0_ini
    gamma0 = E0 / mass
    beta0 = math.sqrt(1 - 1.0 / gamma0 / gamma0)
    phi_list=[]
    phi_list.append(phi_list_ini)

    dE_list=[]
    dE_list.append(dE_list_ini)

    delta_list=[]
    e_temp=np.array(dE_list_ini)+E0

    dl_ini= np.sqrt(e_temp*e_temp-mass*mass)/p0_ini-1.0
    delta_list.append(dl_ini)

    #nus = math.sqrt(harm * abs(ita) * e_volt / 2 / np.pi / E0_ini / beta / beta)

    for ii in range(turns):
        #yield (phi_list, delta_list)
        pl=phi_list[-1]*1.0
        dEl=dE_list[-1]*1.0
        dEl +=  e_volt * (np.sin(pl) - sin_phi_s )

        if energy_change:
            E0 += e_volt * sin_phi_s
            p0 = np.sqrt(E0 * E0 - mass * mass)

        dl = np.sqrt((E0 + dEl) * (E0 + dEl) - mass * mass) / p0 - 1
        gamma0 = E0 / mass
        beta0 = math.sqrt(1 - 1.0 / gamma0 / gamma0)

        if update_eta:
            delta_gamma = dEl / mass
        else:
            delta_gamma =0


        eta = alphac - 1.0/(gamma0+delta_gamma)/(gamma0+delta_gamma)

        if ii > gamma_jump[0] and ii < gamma_jump[1]:
            eta += gamma_jump[2]


        pl += 2.0 * np.pi * harm * eta * dl

        if ii == phase_jump[0]:
            pl += phase_jump[1]
        phi_list.append(pl)
        dE_list.append(dEl)
        delta_list.append(dl)

    return np.vstack(phi_list), np.vstack(dE_list), np.vstack(delta_list)


'''

E00=100e9
mass=938e6
gamma=E00/mass
beta=pylab.sqrt(1-1.0/gamma/gamma)

eV=5e6
alphac=0.002
gammat=pylab.sqrt(1/alphac)

h=360
ita=alphac-1/(E00*E00/mass/mass)
ita0=ita
print(ita)
nus=pylab.sqrt(h*abs(ita)*eV/2/pylab.pi/E00/beta/beta)
print(nus)


turns=5000
#inideltas=[0.001, 0.003, 0.008, 0.013, 0.017, 0.0175]
#iniphis=[phi_s, phi_s, phi_s, phi_s, phi_s, phi_s]
inideltas=[0.003]
iniphis=[phi_s, phi_s, phi_s,-pylab.pi*0.5,pylab.pi-phi_s]
#iniphis=[phi_s, phi_s, phi_s,pylab.pi*1.5,pylab.pi-phi_s]
for id in range(len(inideltas)):
    ini_delta=inideltas[id]
    ini_phi=iniphis[id]
    deltalist=[ini_delta,]
    philist=[ini_phi,]
    plotlist=[0,]
    E0=E00
    mass=938e6
    gamma=E0/mass
    beta=pylab.sqrt(1-1.0/gamma/gamma)
    beta0=beta
    eV=5e6
    relative_omega=1
    alphac=0.002
    gammat=pylab.sqrt(1/alphac)

    h=360
    ita=alphac-1/(E0*E0/mass/mass)
    for i in range(turns):
        dE0=deltalist[-1]*E0*beta*beta
        #dE0=deltalist[-1]
        phi0=philist[-1]

        dE1=dE0+eV*(pylab.sin(phi0)-pylab.sin(phi_s))
        oldE0=E0
        E0+=eV*pylab.sin(phi_s)

        delta_omega=-ita*relative_omega*(E0-oldE0)/oldE0/beta/beta
        relative_omega+=delta_omega
        gamma=E0/mass
        beta=pylab.sqrt(1-1.0/gamma/gamma)
        delta1=dE1/(E0*beta*beta)

        ita=alphac-1/gamma/gamma
        phi1=phi0+2*pylab.pi*h*ita*delta1
        plotlist.append(dE1/relative_omega)
        deltalist.append(delta1)
        philist.append(phi1)

    pylab.plot(philist[1:],plotlist[1:])
    pylab.plot(philist[0:1],deltalist[0:1],'r+')


pylab.xlabel("phase")
pylab.ylabel("energy deviation")
pylab.title('Turn {}'.format(turns))
#pylab.xlim([-pylab.pi/2,1.5*pylab.pi])
#pylab.ylim([-0.02,0.02])
pylab.show()

'''