16: Particle Accelerators

Example number 16.1, Page number 305

In [4]:
#import modules
import math
from __future__ import division

#Variable declaration
fo=9*10**6;    #frequency(Hz)
m=6.643*10**-27;    #mass(kg)
e=1.6*10**-19;      #the charge on electron(C)

#Calculation
Q=2*e;           #electron charge(C)
B=fo*2*math.pi*m/Q;      #magnetic flux density(Wb/m^2)

#Result
print "magnetic flux density is",round(B,2),"Wb/m^2"

magnetic flux density is 1.17 Wb/m^2

Example number 16.2, Page number 305

In [6]:
#import modules
import math
from __future__ import division

#Variable declaration
B=0.7;      #magnetic flux intensity(Wb/m^2)
m=3.34*10**-27;     #mass(Kg)
e=1.6*10**-19;      #the charge on electron(C)


#Calculation
Q=e;
fo=B*Q/(2*math.pi*m*10**6);       #cyclotron frequency(MHz)  

#Result
print "The cyclotron frequency is",round(fo,1),"MHz"

The cyclotron frequency is 5.3 MHz

Example number 16.3, Page number 306

In [9]:
#import modules
import math
from __future__ import division

#Variable declaration
B=0.75;      #magnetic flux intensity(Wb/m^2)
m1=1.67*10**-27;    #mass(Kg)
m2=3.31*10**-27;    #mass(Kg)
e=1.6*10**-19;      #the charge on electron(C)
Rm=2;        #radius(m)

#Calculation
Q=e;
Emax_m1=3.12*10**12*B**2*Q**2*Rm**2/m1;       #Maximum energy for proton(MeV)
Emax_m2=3.12*10**12*B**2*Q**2*Rm**2/m2;       #Maximum energy for deuteron(MeV) 

#Result
print "Maximum energy for proton is",round(Emax_m1),"MeV"
print "Maximum energy for deuteron is",int(Emax_m2),"MeV"

Maximum energy for proton is 108.0 MeV
Maximum energy for deuteron is 54 MeV

Example number 16.4, Page number 306

In [15]:
#import modules
import math
from __future__ import division

#Variable declaration
mo=9.1*10**-31;      #mass of electron(kg)
m=1.67*10**-27;      #mass of proton(kg)
c=3*10**8;           #speed of light(m/s)
E=1;                 #given energy(MeV)

#Calculation
Eo=mo*c**2/(1.6*10**-13);         #rest energy for electron(MeV)
mbymo_e=1+(E/Eo);                #Ratio for electron
Eo=m*c**2/(1.6*10**-13);          #rest energy for proton(MeV)
mbymo_p=1+(E/Eo);                #Ratio for proton

#Result
print "Ratio for electron is",round(mbymo_e,3)
print "Ratio for proton is",round(mbymo_p,6)
print "answer in the book varies due to rounding off errors"

Ratio for electron is 2.954
Ratio for proton is 1.001065
answer in the book varies due to rounding off errors

Example number 16.5, Page number 306

In [20]:
#import modules
import math
from __future__ import division

#Variable declaration
B=0.5;      #magnetic field(Wb/m^2)
d=1.5;      #diameter(m)
f=59;       #frequency(Hz)
e=1.6*10**-19;        #the charge on electron(C)
c=3*10**8;            #speed of light(m/s)

#Calculation
R=d/2;             #radius(m)
N=c/(4*(2*math.pi*50)*R);       #number of revolutions
E=B*e*R*c/(1.6*10**-13);        #final energy(MeV)
AE=E/N*10**6;                 #average energy(eV)

#Result
print "final energy is",E,"MeV"
print "average energy is",round(AE,1),"eV"
print "answer for average energy given in the book is wrong"

final energy is 112.5 MeV
average energy is 353.4 eV
answer for average energy given in the book is wrong

Example number 16.6, Page number 307

In [30]:
#import modules
import math
from __future__ import division

#Variable declaration
E=0.51;      #kinetic energy(MeV)
R=0.15;      #radius(m)
e=1.6*10**-19;      #the charge on electron(C)
mo=9.12*10**-31;    #mass of electron(kg)
c=3*10**8;          #speed of light(m/s)

#Calculation
Eo=E;
m=mo*(1+(E/Eo));       #mass(kg)
b=math.sqrt(1-(mo/m)**2);
v=b*c;            #velocity(m/s)
B=mo*v/(e*R);     #flux density(Wb/m^2)   

#Result
print "mass is",round(m/1e-31,1),"*10^-31 kg"
print "velocity is",round(v/1e+8,1),"*10^8 m/s"
print "flux density is",round(B,5),"Wb/m^2"
print "answer for flux density in the book varies due to rounding off errors"

mass is 18.2 *10^-31 kg
velocity is 2.6 *10^8 m/s
flux density is 0.00987 Wb/m^2
answer for flux density in the book varies due to rounding off errors

Example number 16.7, Page number 308

In [33]:
#import modules
import math
from __future__ import division

#Variable declaration
E=4;       #applied voltage(MeV)
m=3.334*10**-27;      #mass of deuteron(kg)
R=0.75;               #radius(m)
e=1.6*10**-19;        #the charge on electron(C)

#Calculation
E=4*10**6*e;
fo=math.sqrt(E/(2*m))/(math.pi*R);     #frequnecy of generator(Hz)

#Result
print "frequnecy of generator is",round(fo/1e+6,3),"*10^6 Hz"

frequnecy of generator is 4.158 *10^6 Hz

Example number 16.8, Page number 308

In [36]:
#import modules
import math
from __future__ import division

#Variable declaration
roi=15;      #rate of increase(Wb/s)
tr=10**6;    #total revolutions

#Calculation
IE=roi*10**-6;      #increased energy(MeV)
FE=IE*tr;           #Final Energy(MeV) 

#Result
print "Final Energy is",FE,"MeV"

Final Energy is 15.0 MeV

Example number 16.9, Page number 308

In [43]:
#import modules
import math
from __future__ import division

#Variable declaration
R=0.1;       #radius(m)
h=6.625*10**-34;        #Plank's constant
c=3*10**8;              #speed of light(m/s)
roi=15;                 #rate of increase(Wb/s)
t=4*10**-4;             #period of accerleartion(s)
e=1.6*10**-19;          #the charge on electron(C)

#Calculation
N=c*t/(2*math.pi*R);      #number of revolutions
IE=roi;              #incresed energy(eV)
ME=N*IE*10**-6;      #maximum energy(MeV)  
ME1=ME*10**6*e;       #conversion in V
p=ME1/c;
gama=h/p;         #wavelength of gama rays(m)

#Result
print "Maximum energy is",round(ME,3),"MeV"
print "Corresponding wavelength of gama rays is",round(gama/1e-13,3),"*10^-13 m"

Maximum energy is 2.865 MeV
Corresponding wavelength of gama rays is 4.336 *10^-13 m