Engineering aspects of a 2MeV Electrostatic Van de Graaff Electron

Accelerator.

By:

Ramiro G. Rivadeneira

Texas A&M UniversityDepartment of Biological and Agricultural Engineering

Electrostatic Accelerator HistoryPhysicists 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 electrostatic electron accelerator.Such an accelerator uses high-voltage to produce beams of electrons that can be directed to a target.

Fundamentals of Charged Particle Acceleration

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

How do we accelerate a particle?In order to accelerate a particle:

Its kinetic energy E needs to increase. How?By change in its momentum P. Therefore a charged particle is accelerated when a change in its momentum occurs, produced by an electric field E.Then:

Now, consider an electron traveling between two parallel plates at a potential difference V.

xxx qEF

dtdP

==]1[

The force Fx (Lorentz Force) experimented by the electron is given by:

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

F=qE

me , q

vx

Uniform Electric Field, E

KE1, V1KE2, V2

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

( )EBvqF +×=]2[

Change in Kinetic EnergyAs an electron moves from point 1 to point 2, its kinetic energy changes by:

However, because of the uniform electric field E, the path velocity vector vx is parallel to the path vector dr, then the cross product (v x B) dr = 0

It can be seen that magnetic fields then do not change the particle energy E, thus particle acceleration depends only on the uniform electric field E.

drEBvqdrFEr

r

r

r

⋅+×=⋅=∆ ∫∫2

1

2

1

)(]3[

Thus, simplifying [3]

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:

Thus, the uniform electric field E can be calculated given V and d.

∫ =⋅=∆2

1

]4[r

r

qVdrEqE

dEVV ⋅=− 21]5[

Using kinematics and Einstein's mass energy postulates to recognize that electrons are high-velocity particles; then:

emeEtts2

)(]5[2

=em

eEttv =)(]6[em

eEta =)(]7[

x

y

z

me

vx

d

(0,0)

E

Voltage, Beam Current, and Power

Given the physics of electron acceleration due to uniform electric fields, it is possible to formulate expressions to define the voltage at the high terminal V (potential difference between the two plates), electron beam current I, and beam power P.The following graphic is a circuit representation of the Van de Graaff electron accelerator:

Thus, the potential difference at the high voltage terminal is:

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 densitypresent in the charging belt. Thus:

CtIV =]6[

Current Beam IObtained 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:

Charge density, [C/cm2]

Charged belt width a [cm]

Beam current I [A]

Charged belt velocity v

[cm/s]

vaI σ=]7[

Maximum Electric field and Environment Dielectric Strength

The maximum electron density on the belt depends on the permissivity of the surrounding and the maximum electric field before breakdown. Then for a flat rubber belt:

Where Emax is the maximum uniform electric field. In fact, for an electron traveling between parallel plates:

maxmax 2]8[ Eoεεσ =

dEV ⋅= maxmax]9[

Voltage Breakdown

Beam Power

The power of an electron beam is obtained as:

It results from electrons overcoming the strength of the uniform electric during the conveying of the charged particles.

Given all the physical parameters, it is possible to describe the machine components from a technical viewpoint.

VIP =]8[

Physical and Technical Description• The VDG accelerator is analyzed in 3 main

components:1. Van de Graaff High Voltage Generator

• Drive motor• Charging belt• The Column• High voltage terminal

2. Vacuum System• Electron accelerator tube system

3. Control panel

Electrostatic Van de Graaff System Layout

Circuit Scheme of a Van de Graaff Electrostatic Accelerator

In this scheme, three main terms need to be recognized.Van de Graaff Generator, and charging belt.Accelerating ColumnVacuum tube

Component Analysis

1.1. Van de Graaff High Voltage Generator

Circuit composed of a drive motor, a charging belt, voltage-generating column, high voltage terminal, generating voltmeter.Works at potential difference V, and this is where the high-voltage is produced by transporting electrons thru the charging belt.Usually, a 20:80 mix of CO2 and Nitrogen at 150-200 psi is used to maximize Vmax.

1.2. The Charging Belt

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

1.3. The Column

Composed of aluminum equipotential rings.Potential difference of 47 kV per plane in the column. Voltage across column is divided using a voltage divider (remember VT=IRT) where each resistor supports 900 M . This is done to achieve a uniform charge distributionacross the belt.

Voltage Generating Column

Voltage Generating Column-Full View

1.4. High Voltage Terminal

It is made of metal hemispheric shell:Highly polished to prevent electric stressesConnected mechanically and electrically to terminal plate.Range: 0.75 to 2 MeV

Showed on previous picture.

2. Vacuum SystemUsed 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 the range of: 1x10-6 to 30x10-6 mm Hg maximum.

2.1. The electron accelerator tube system

Electrons are transmitted through a cathode from the column to the tube system. They travel free at constant acceleration, due to the constant voltage gradient V, in the column.An Exit portal can produce beams of electrons of circular diameter (0.4 in or 1.0 cm). This beam can be focused up to 10X its magnitude, i.e, 0.04 in.

The electron accelerator tube system

NOTE: Electrons beams may be deflected by external magnetic fields

3. The Control Console.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.

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)

Discussion: Advantages Continuous Operation

Provide constant beam current IUniform beams due to equipotential column layout.

Able to produce beams of positrons and x-rays.Plenty of industry applications mainly in:

Environmental: disinfect waste water & solids.Biomedical: sterilization of materials.Metallurgic: material hardeningMost recently Food

Applications in the Food Industry

Low energy electron beams great for food applications specially in fruits and vegetables where only surface radiation is required. Applications include:

DecontaminationSprout InhibitionIncreased shelf-lifeProduct functionality improvement.Reduction of pathogenic bacteria.

Discussion: Disadvantages

Low energy applications only.Needs external stabilizing circuit system to maintain a uniform voltage distribution.

Charging belt is not the best device to transport charges. Conveying systems made of steel produce a more uniform charge distributionThus better voltage control. (See Pelletron)

Old Van De Graaffs occupies lots of physical space.

New designs include vertical designs for enhanced 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.