Basic Processes in Electron Acceleration-Accelerator Physics-Lecture Slides, Slides of Accelerator Physics

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BASIC PROCESSES IN

ELECTRON ACCELERATION

THE ACCELERATING

WAVEGUIDE

Lecture 9

Linear Accelerator

Electron Accelerators

• 6 MV short waveguide

No bending

magnet

Electron Accelerators

• 18 MV long waveguide

Linear accelerators (1/2)

 electrostatic accelerators

positive ion beam energy = 2qV n+

Analysing Magnet

Charging belt negative ion source

high voltage terminal V ≤ 10 MV

Stripping foil

- (^) n+

(n-1)+

(n+1)+

tandem Van der Graaf, pelletron is one good example.

Linear accelerators

 RF linac Wideroe (1928)

V=V 0 *sin(t)

Alvarez (1946)

V=V 0 *sin(t)

Focusing magnets

Focusing magnets

• A positively charged particle traveling along the axis of the tubes in the diagram can be accelerated from left to right if it passes through the gap between the first and second tubes when the polarity of the voltage is as shown.
• If the time required for the particle to pass through the second tube is equal to one half cycle of the alternating supply, then the electric field between the second and third tubes will be in the direction to accelerate the particle further.

Waveguides

• This process can then give energy to the particle as it passes through each gap in a long series of tight tubes.
• However the lengths of successive tubes must be increased so that the transit time of the accelerating particle remains equal to the half period of the alternating supply.
• A system using a radiofrequency supply and medium-atomic- number particles can form the basis for a practical linear accelerator, as demonstrated by Wideroe (1928) and Sloan & Lawrence (1931).
• This technology is not practicable for accelerating electrons because the high velocity attained by these very light particles would require the use of excessively long flight tubes where a radiofrequency (RF) supply is used.

WAVEGUIDE THEORY

• If an electromagnetic wave is transmitted between conducting surfaces, then it is reflected at these surfaces as shown in figure 2.2(a).
• These waves interfere and energy will only be transmitted along the axis if the instantaneous interference patterns between the reflecting surfaces are coherent.
• This can happen only if the path length between reflections AB in figure 2.2(a) is an integral number of wavelengths.

(a) The central ray of an electromagnetic wave being reflected between parallel conducting surfaces.

(c) Instantaneous electric field distribution

(b ) Instantaneous electric field. The arrows indicate the direction of the electric field

WAVEGUIDE THEORY

• For a particular separation of the conducting planes, the

length AB can meet the condition of being an integral

number of wavelengths for a number of different angles

between AB and the axis of symmetry;

• Such modes are only possible if the wavelength is less

than a cut-off wavelength, which is related to the

separation of the conducting planes.

• As the waves progress between the conducting planes

by a series of reflections in the electric field, which

would be normal to the direction of propagation in free

space, now has an axial component, which we will see

can be used to accelerate electrons.

Dielectric Waveguide

Let us consider the simpler case of a rectangular slab of waveguide.

 r  i (^)  r

 1     1 1 and 2    2 2

Snell’s Law of Reflection

1 2

sin

sin

t i

^   

Snell’s Law of Refraction

  1 2 1

i (^) critical^ sin^ r r

  

  ^ 

Critical Angle:

Case(1):   i   i  critical

Case(ii):   i   i  critical

When the incident angle is greater than the critical angle, the wave is totally reflected back and this phenomenon is known as Total internal reflection.

Total internal reflection

Incident wave (^) Reflected wave

Refracted wave

Incident wave

Velocity of light in Free Space Velocity of light in the medium (^) u^ r^ r

c n u

    

Dielectric Waveguide

The index of refraction , n , is the ratio of the speed of light in a vacuum to the speed of light in the unbounded medium, or

In nonmagnetic material n   r

  1 2 1

i (^) critical^ sin

n n

1 2

sin sin

t i

n n

1 1 1 1 u o r o r o o r r r r

u^ c           

   

1 o o

c  



  r 1

Where

Critical Angle:

Snell’s Law of Refraction:

Snell’s Law of Refraction can be expressed in terms of refractive index:

Index of refraction: