By:

Accelerator. Texas A&M University Ramiro G. Rivadeneira

ment of Biological and Agricultural Engineering

Engineering aspects of a 2MeV Depart

Electrostatic Van de Graaff Electron to that can be

high-voltage

electrostatic electron

target.

beams of electrons Physicists developed machines capable of accelerating particles to study particle interactions from non-radioactive materials in the early 1900’s. R.J. Van de Graaff, an American scientist, in 1931 invented the Such an accelerator uses produce accelerator. directed to a Electrostatic Accelerator History „ „ „ used by the Van

particle dynamics.

Fundamentals of Charged Particle Acceleration

The study of particle beams any kind is called This branch of physics will make it possible to understand the principles of accelerating electrons de Graaff particle accelerator. „ „ .

E in its Therefore a charged

change x P. qE = x F = x dt dP ] 1 [ Its kinetic energy E needs to increase. How? By change in its momentum Then: Now, consider an electron traveling between two parallel plates at a potential difference V. momentum occurs, produced by an electric field particle is accelerated when a

How do we accelerate a particle? In order to accelerate a particle: „ „ „ „ Uniform Electric Field, E

KE , V KE , V 2 2 1 1 F=qE vx

me , q

Fig 1. Electron acceleration in a uniform electric field E between two parallel plates.

„ The force Fx (Lorentz Force) experimented by the electron is given by: [2] F = q(v × B + E)

„ Where E is a uniform electric field between plates, and B is a magnetic field. vector

path dr ⋅ ) E dr = 0 + B × v x B)

( E, thus particle 2 1 ∫ r r v  q = is parallel to the dr

⋅ x v F 2 1 ∫ r r = E ∆ ] 3 [

Change in Kinetic Energy then the cross product (

As an electron moves from point 1 to 2, its kinetic energy changes by: However, because of the uniform electric field E, path velocity vector dr, It can be seen that magnetic fields then do not change the particle energy acceleration depends only on the uniform electric field E. „ „ „ „ Thus, simplifying [3]

r 2 [4] ∆E = q ∫ E ⋅ dr = qV r1

„ Where V is the potential difference between plates.

„ In fact for a two parallel plates between a uniform electric field separated by a distance d, it follows that:

[5] V1 −V2 = E ⋅ d

„ Thus, the uniform electric field E can be calculated given V and d. „ Using kinematics and Einstein's mass energy postulates to recognize that electrons are high- velocity particles; then:

y E

vx (0,0) x

me d

z eEt 2 eEt eE [5] s(t) = [6] v(t) = [7] a(t) = me me 2me .

P , it is possible to (potential difference

V , and beam power I

uniform electric fields formulate expressions to define the voltage at the high terminal Given the physics of electron acceleration due to The following graphic is a circuit representation of the Van de Graaff electron accelerator: between the two plates), electron beam current „ „ Voltage, Beam Current, and Power „ Thus, the potential difference at the high voltage terminal is: It [6] V = C „ Where C is the capacitance of the high-voltage electrode, t conveyor operating time.

„ The beam current I is obtained in terms of the electron charge density present in the charging belt. Thus: " ] 2 C/cm Charge [ density, v ] σ a cm = I ] 7 Charged belt width a [ [ I v ] ] A [ cm/s [ velocity Charged belt Beam current

Current Beam I Obtained in terms of transport belt charged density. The steady-state current for accelerating electrons is equal to the current transported by the transport belt. Thus: „ „ max on the belt depends d E ⋅ o ε max ε E 2 = = max max

σ V ] ] 9 8 [ [ is the maximum uniform electric field. In max

maximum electron density The on the permissivity of surrounding and maximum electric field before breakdown. Then for a flat rubber belt: Where E fact, for an electron traveling between parallel plates:

Maximum Electric field and Environment Dielectric Strength „ „ Voltage Breakdown the

overcoming V I = P ] 8 [ The power of an electron beam is obtained as: It results from electrons Given all the physical parameters, it is possible to describe the machine components from a technical viewpoint. strength of the uniform electric during conveying of the charged particles.

Beam Power „ „ „ r o t o m e v i r igh voltage terminal harging belt he Column lectron accelerator tube system C T E H he VDG accelerator is analyzed in 3 main components: •D • • • • T Van de Graaff High Voltage Generator Vacuum System Control panel • 1. 2. 3. Physical and Technical Description Electrostatic Van de Graaff System Layout In this scheme, three main terms need to be recognized. Van de Graaff Generator, and charging belt. Accelerating Column Vacuum tube „ „ „ „

Circuit Scheme of a Van de Graaff Electrostatic Accelerator Component Analysis max. V and Nitrogen 2 at 150-200 psi is used to maximize Circuit composed of a drive motor, charging belt, voltage-generating column, high voltage terminal, generating voltmeter. Works at potential difference V, and this is where the high-voltage produced by transporting electrons thru the charging belt. Usually, a 20:80 mix of CO „ „ „ 1.1. Van de Graaff High Voltage Generator , equal to from ground to the high-voltage

1.2. The Charging Belt

steady state current I is produced terminal. High quality rubber belt. Works at a static tension of 200 lbs maximum. Provides a medium for electrons to be At the ground potential side of belt, electrons are transferred onto the belt thru an outside voltage source working at a potential of approximately 7kV. A transported the beam current produced at acceleration tube. „ „ „ „ ) T =IR T

1.3. The Column .

Composed of aluminum Potential difference of 47 kV per plane in the column. Voltage across column is divided using a voltage divider (remember V This is done to achieve a across the belt. equipotential rings. where each resistor supports 900 M uniform charge distribution „ „ „ „ Voltage Generating Column Voltage Generating Column-Full View Highly polished to prevent electric stresses Connected mechanically and electrically to terminal plate. Range: 0.75 to 2 MeV „ „ „ It is made of metal hemispheric shell: Showed on previous picture.

1.4. High Voltage Terminal „ „ mm Hg -6 to 30x10 -6

2. Vacuum System Used to provide a path free for electrons to move Thus, electrons can be accelerated without losing energy, until they reach a target or an exit portal. A mercury vacuum pump is used and the normal operating pressure is in range of: 1x10 maximum. „ „ „ beams of of circular diameter (0.4 in or from the column to tube 1.0 cm). This beam can be focused up to 10X its magnitude, i.e, 0.04 in. Electrons are transmitted through a They travel free at constant acceleration, due to the constant voltage gradient V, in the column. An Exit portal can produce cathode system. electrons 2.1. The electron accelerator tube system „ „ „ The electron accelerator tube system Electrons beams may be deflected by external magnetic NOTE: fields All the parameters analyzed so far can be controlled by means of external circuits. Most importantly the desired voltage, and beam current can be regulated. All devices such as motors, voltmeters, and calibrating devices are linked to the control console.

3. The Control Console. „ „ „ Fundamental Operating Principles

1. Charged particles accelerated due to potential difference between high voltage terminal (HVT) and ground.

2. Electrons conveyed to the HVT thru the top of a conveyor belt.

3. At the end of the HVT terminal electrons are collected until the desired potential difference is obtained. Fundamental Operating Principles

4. Finally electrons are transmitted to the acceleration tube through a cathode head, and thus accelerated to the desired potential under vacuum.

5. Finally electrons form a beam with current I, due to the electrostatic uniform electric field E, thus potential difference V. (Remember V=Ed) x-

I Provide constant beam current Uniform beams due to equipotential column layout. Environmental: disinfect waste water & solids. Biomedical: sterilization of materials. Metallurgic: material hardening Most recently Food Discussion: Advantages „ „ „ „ „ „

Continuous Operation Able to produce beams of positrons and rays. Plenty of industry applications mainly in: „ „ „ great for Decontamination Sprout Inhibition Increased shelf-life Product functionality improvement. Reduction of pathogenic bacteria.

Applications in the Food Industry „ „ „ „ „

Low energy electron beams food applications specially in fruits and vegetables where only surface radiation is required. Applications include: „ Charging belt is not the best device to transport charges. Conveying systems made of steel produce a more uniform charge distribution Thus better voltage control. (See Pelletron) New designs include vertical for enhanced space.

Discussion: Disadvantages „ „ „ Low energy applications only. Needs external stabilizing circuit system to maintain a uniform voltage distribution. Old Van De Graaffs occupies lots of physical space. „ „ „ Conclusions: What you should know.

„ Electrostatic accelerators are machines that use high voltage to produce beams of electrons. „ High voltage is produced by moving charged particles across a potential difference, and a uniform electric field. „ Uniformity of the potential difference depends on the distribution of charge within the charged belt. „ Acceleration of particles is dependent on the stability of the voltage generated.