PART 1 LECTURE 1 page no HCMUNS 2013.pdf

8/10/2019 PART 1 LECTURE 1 page no HCMUNS 2013.pdf

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Introduction for Mo dern ccelerators

Pr inciple and its pplication

Takahisa I tahashi

Visi ting Professor,

UNI VERSITY of SCIENCE-VNUHCM,Faculty of Physics and Nuclear Technology

Part 1, Accelerators, Principle and Components

Part 2, Applications of Accelerators

Lecture guide are shown in several slides at the class,

They include such as references, required courses,

and credits ----.

You will have occasionally small exams, after the end

of class and you will have to present reports


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Chapter 1. Accelerator and i ts pr inciple

1.1 I ntroduction

Accelerators were developed along with a realization of scientific curiosity in

Nuclear Physicsand in Elementary Physics

Scientific innovations have been brought about with advanced technologies in

Accelerator Science and Technologies.

These works have been more widely applied to various scientific subjects such as

Biology, Archeology, Astrophysics, Medical Science, Environmental Science and so

on.

Developments of compact and cost-effective accelerator are really crucial for these

studies

In Particle Physics new particles and ideas have been brought about by the

development of accelerators and various detectors

You should remember these developments to cope with the difficulties in existing

technologies; super-conducting magnet, RF cavities, ion source, and so on.

Realized ideas have been appeared in the several lectures in undergraduate courses;

such as Analytical Mechanics, Electricity and Magnetism.

Today cost effective and compact accelerators are needed in various scientific fields;

medical applications and nano-technologies.

This lecture includes the fundamental aspects of accelerator principle and I will focus

the physics ideas appeared in the specific performances of applied fields.

The main parts are concerned with Cyclic Accelerators and the other also with

Static Accelerators

The Linear Acceleratorwill be briefly mentioned about, and the references will belisted up.


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Various words appeared in this lecture are

What is a charged particle?

Ionization Figure Ions

What is an accelerator?A machine for which a charge particle can be accelerated and transported by using the

Coulomb and /or Lorentz forcesto increase the particle energy

Components of the accelerator

Production Ion source

Transport Beam line

Acceleration >>> Transport>>> Beam line

Irradiation Target

Motion in the Electric FieldMotion in the Magnetic field

What is an ion beam?

An ion beam is a flow of energetic ions, similar to the light.

Figure

Unit of the Energy,

Energy-Mass Equivalence Priciple

= +

= Through their Electromagnetic Interaction, Particles are accelerated.

Only electrically charged particles that are stable may be readily accelerated.

All accelerators must have a sour ce of charges, a means for accelerating the charges, and

an evacuated ----.

Besides the particle species,the two parameters the energy and the particle flux.

The particle flux in an experiment is often referred to as the luminosity.

From the definition of cross section the rate(R) of event for a particular process,the

luminosity (L ) times the cross section (

) for that process:

R = L

The units of luminosity are m-2s-1

= =

9.1110 .

x .5.11x10 = 0.511

For proton, try the same ways ?


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1.2 Birth of accelerator

It was based on the following background

Curiosity for nature -> invisible things-> The discovery of natural radio-activities

Chemical properties (periodic table) -> logical ways ->Matter->molecule-> atomObservation of Cosmic ray (Hess received Nobel Prize in 1935) -> other direction from

accelerator->has become an interesting field of science

Natural particle sources such as Alpha-, beta-, gamma-, decays ->(means, expectation)

existing of internal structure, tiny constituents

As a tool,

Statistics and systematic would be not enough compared with laboratory

measurements, it will be experienced if you start the some studies

Reproduction and confirmation would be not so easy to realize the sameexperimental condition

Model would be so sophisticated as not to elucidate the phenomena happened

in the studies

We need accelerators

I on source, acceleration, potential, high voltage,

We can assign an electric potential energy U to the system .

We usually set the corresponding reference potential energy

to be zero. The potential difference is actually discussed


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The acceleration principles are based uponthe Classical Electricity and Magnetism

By considering the acceleration, there appeared two types of accelerators such as

DC-accelerator and AC-accelerator

DC accelerator has a severe limit

to the obtainable energy due to the

applied voltage

The motion of Charged Particles

in the Electric Field

Acceleration of charged Particles

Deflection of Charged Particles

Focusing of Charged Particles

F= q E


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1.3 I ntr oduction of DC-Accelerator

1.3.1 Energy Units

The energy units of modern physics are derived from the unit of potential

difference in electricity, the volt(V). The definition of the volt is

1 V 1 J/C1 J = 1V1C [ e

.

]

= e.= e

.

1 eV = 1.602x10J The electric force constant kin Coulombs law is measured

to be 8.99 x 109Jm/C2. Calculate the quantityke2in units of (Jm)

and (eVnm).

ke2= 8.99 x 109 J m/C1.602x10C = 2.30x10

-28J

And k=(../e) n

= 1.44 eVnm Calculate the strength of the electric field at a distance of 0.1 nm frm a proton

E=

= =

.44 ene.n

=144 v/nm = 1.44x1011V/m this electric field is an extraordinaly big comparedwith to fields accessible in the laboratory.

Cathode ray tube

The apparatus is a kind of accelerator

By the way, do you know G.P. Thomson ?

Remember J.J.Thomson experiment for

discovery of electron

With C.J. Davissonhe receivedNobel-Prize

foran electron diffraction

Note the polarity of electron source, cathode

potential

I suppose E-field would be moreeasier and familiar to deal with at

that period, 1930


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1.3.2Mass Energy

Consider the b particles (electrons) from the spontaneous decay of a heavy nuclei

first observed by Becqurel. These electrons did not exist before the nuclei dcayed.

The electrons are created in the decay process. The electrons are produced with a

typical kinetic energy of an MeV.Where does this energy come from ?

The energy that the electron acquires was stored in the form of mass energy of the

decaying nucleus.

The total energy (E) of any particle is defined to be the sum of two parts: energy due

to motion, called the kinetic energy (Ek), and Energy stored in mass, called the mass

energy (E0). Energy is defined in this manner,

+ Because this quantity is observed to be conserved in all particle interactions. =

c3.00x10 m/sThe electron mass energy is

= = 9.1110 3.00x10 s

x .

5 . 1 1 1 0eV = 0.511

1. Similarly, the proton mass energy is ????

2. Calculate the electron mass in units of MeV/c2

3. Show explicitly the MeV/c2has units by expressing it in kgs

4. The atomic number of hydrogen is A=1.00078. Calculate the mass energy of the

carbon atom (A=12) in electron volts. Estimate firstly the atomic mass unit, 1 u.

1.3.3 Binding Energy

Consider an electron and proton bound togather to form an atom of hydrogen.

The energy (E) required to separate the electron and proton to a large distance, work

done against the Coulomb force, is measured to be

E = 13.6 eV

What happens to this energy ?

The energy needed to ionize the hydrogen atom has been converted into mass energy.

The mass energy of the hydrogen atom (mHc2) is smaller than the sum of the mass

energies of the electron(mec2) plus (mpc

2) by an amount equal to 13.6 eV:

mHc2+ 13.6 eV = mec2+ mpc2


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The difference between the mass energy of the components (the electron and the

proton) and the mass energyof the composite object (the hydrogen atom) is called the

binding energy (Eb):

Eb= mec2+ mpc

2mHc

2= 13.6 eV

The binding energy is the amount of energy that must be provided inorder to break theatom into its components. When this happens, the fractional change in mass (mH/mH) of

the atom is

=

=

13.6 9.3910 10

For most processes, we may neglect this change in the mass of the atom.

The experiment of J.J.Thomson


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1.4 Cockcroft-Walton Type Accelerator

DC accelerator has been still used as an injector of the big accelerators, One of the

most valuable dc accelerator, well developed components such as capacitors, resistors,

and various protection parts

Q. Why do we use these old ideas until now ?

Ans. Good beam quality

Well established techniques

Simple assembly

Easy maintenance

Old times 1930

1990 at PSI


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Laboratory Exper iments by Cockrof t and Walton

With the first proton accelerator, Cockroft and Waltonobserved the reaction

p +7Li -> +.

Make an order-of-magnitude estimate of the proton energy required to initiate the

reactionp + 7Li -> +.First consider conservation of energy. If the prton has zero kinetic energy, then the Q

value of the decay is

Q = mpc2+ mLic

2mc

2mc

2

or

Q = 938.3 MeV + 6533.9 MeV3727.4 MeV3727.4 MeV ~ 17 MeV

The Qvalue is positive, positive, so conservation of energy does not place a limit on

the proton energy threshold. The energy threshold limit comes from the Coulomb

barrier presented by the7

Li nucleus. If R is the nuclear radius, the energy thresholdfor the proton to surmount this barrier is

=

=

be careful for h= h/2here.

If we estimate R to be about 2 fm and use Z=3 for lithium

Ek= 7 3 (

) = 2 MeVThus, the order of magnitude of the proton kinetic energy needed to cause the nuclear

reaction is 2 MeV.

Wave Nature-----


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1.4.1 The structure of Cockcroft-Walton Accelerator

Fig 3.1 appeared in pp. 243 (a) schematic

representation of a cascade of C-W double circuits

(J.B.A. England )

The network A0, A1, B0, B1, C0, C1, D0and D1constitutes a single-voltage doubling stage and by

operating several such stages in cascade a

corresponding increase in voltage is obtained at the

points A in these stages. Initially all the capacitors

are uncharged so that the voltages of all points -----.

1.4.2 The pri nciple of C-W accelerator

In this single voltage doubling stage during thefirst cycle of operation, assuming that no further

stages are coupled to it.

Suppose that in the first half-cycle the point B0is

negative with respect to A0.

The point B1attempts to follow point B0and, since C0is uncharged, it becomes negative

with respect to A0so that D0conducts and point B1stays close to the voltage of point A0.

The capacitor C0is thus charged to a total charge Q at the voltage V, where Q = C0V.

This charging occurs so long as point B1

is slightly negative with respect to A0

, that is,

during the first quarter of the cycle.

Once the voltage of B0passes the peak negative voltage, -V, and starts to rise

towards zero volts, B1rises above A0, because C0 is now charged to a voltage +V, and D0

cuts off. However, because A1is initially at the same voltage as A0, B1is now rising

above A1in voltage and so D1 conducts and part of the charge Q on capacitor C 0flows to

A1so that C1is now charged D1continue to conduct so long as B1is at a higher voltage

than A1, that is, from the end of the first quarter of the cycle to the end of the third quarter.

Once B0passes the peak positive voltage, +V, and starts to fall towards zero volts, D1

ceases to conduct and B1follows B0down until the voltage of B1passes zero volts when

D0again conducts and C0is then recharged to the voltage +V. The process is repeated and

after a few cycles the points A1, B0and B1 with time over the first few cycles is shown in

figure. Figure 3.1 (b).


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1.5 The Van de Graaff generator

The electrostatic generator was conceived by Load Kelvin in 1890 and put into useful

practice in essentially its modern form by R. J. van de Graaff in 1931. Later this has been

changed into the Pelletron Accelerator by Herb (NEC)

Electric charge is an intrinsic characteristic of the fundamental particles

making up those objects. There are two types of charge.

charge


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1.5.1 Principle based on Electricity and Magnetism

Gausss Law

= 4 +

= 4 +

(VrVR ) =

4

> 0 ( q> 0

Vr= VR Vr- VR = 0=

4

Inner and outer conductors will be connected, and then what happen ???

1.5.2 Negative ion and positive ion; charged parti cles

What are they?

How do you make them?

These basic ideas are based on the collision of atoms with electrons

Neutral atoms collides with energetic electrons, bound electrons may easily stripped off,

or attached to and become charged particles, either positive or negative.

This is positive ion source

The other is negative ion source

The principle of positive ion source

Consider the electron of Hydrogen atom

The centrifugal force due to the Coulomb interaction between the electron and Hydrogen

nuclei, proton

mv2/r = e

2/4e0r

2

Bohrs theory for Quantum Theorem,

mvr= nh/2, n = 1,2,3, ----

Discrete radius of electron orbit is described asrb= (e0h

2/me

2) n

2= a0n

2

V_R

++++++

Q

+q+q+qq

Two conducting spheres

Connect each other equi potential not zero


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r1= a0= e0h2/me

2= 0.529 [Ao] Bohr radius

Total energy (W) of electron in these orbit is the sum of the kinetic energy (Tn) and

potential energy (Ue)

Tn= 1/2 mv2= e

2/8e0rn

Coulomb potential at radius rnV = e/4e0rn

Thus the potential energy of electron is

Ue = - e2/ 4e0rn

The total energy

Wn= Tn+ Un= - (e2/8e0a0) 1/n

2

Winf= 0

Wi = WinfW1= 13.6 [eV]

We= WnW1= (e2

/8e0a0)(11/n2

)Wn= - Ze

2/8e0a0(1/n

2)Z

2e

2/8e0a0(1/n

2)

Wi= WinfW1= Z2e

2/8e0a0

1.5.3 Basic Pri nciples of the Char ging Systems

The basic method for transferring charge to the final high voltage terminal in a Van de

Graaff type of electrostatic generator is a mechanical one.

Three different versions of this mechanical transport system are currently in operation.

The insulating endless belt

The Pelletron type of charging system


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High voltage

Basic principle of the charging systems

The method for transferring charge to the final

high-voltage terminal in a Van de Graaff type of

electrostatic generator is a mechanical way;

three different versions of this mechanical

transport systems are currently in operation.

The most widely used method is the insulating endless belt.

Molded rubberized fabric.

Uniform insulating properties

The belt and pulley system serves the dual purpose of transporting charge to the

terminal and of providing a source of low voltage power inside the terminal for auxulially

or ancillary equipment.

The normal method of placing the charge on the belt is by Corona discharge

This charge placed on the moving belt is then transported to the high voltage terminal

electrode, where it is removed by a second set of corona points or by a wire brush

rubbing on the belt.

The discharge in the gas or in air can provide either positive or negative charge on the

belt.

Charge currents of up to about 1 mA can be transported in this way at a belt speed of

about 25 ms-1

.

The belt charging system in Van de Graaff generators are shown in fig. Fig. 3.3 appeared

in page 255.The pellet system developed later by Herb has more advanced technologies and

advantages,Induction not discharge

Paschen

Law

Discharge in gas

Discharge and holding voltagge

Explain detailLimit of electric potential between 1 cm gap

Air 1 Atm ~ 30 KV

SF6 ~ 80 KV

Insulating oil ~ 150 KV

Vacuum ~ 220 KV

SF6 7 Atm ~ 360 KV

52

SF6 could be used insulator

gas for holding the highvoltage, but it could produce

toxic materials when it

discharged. Be careful!!


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Single ended Van de Graaff


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1.5.4 Tandem accelerators

(1) A terminal voltage V, the final energy {V(1+n)}eV

(2) The ion source and all its controls are outside the pressure vessel and at or near

ground potential.

1.5.5 Tr iple acceleration

Further increasing the final energy of the particles in a purely electrostatic accelerator

system

Only realized is triple three stage Van de Graaff

{V+ V(1+n)}eV

(1) Negative ion produced and accelerated with V

Injected into Tan dem van de Graaff with Vand V(1+n)

In total(2) positive ion produced and accelerated with small single ended machine at about

500 keV

and neutralized and inject into second tandem pass through adder canal in the negative

terminal and becomes negative ions which are then accelerated.

problem of negative helium ion

Positi ve or Negative ion source


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1.5.6 Tan-dem Van de Graaff and negative ions

This is a fur ther development of the Van de Graaff generator.The new feature is to

use the electrostatic potential twice over. First an extra electron is attached to a neutral

atom to create anegative ion. In recent years, there has been considerable development

and it is now possible to obtain negative ion sources for almost all elements (?). The

negative ion beam is injected at ground potential into the tandem. At the high-voltage

terminal the beam passes through a thin foil which strips at least two electrons from eachion converting them to positive ions. They are then accelerated a second time back to

Charge

From negative

to positive

Stripper foils or

gas stripper

SF6high pressure

Gas circulation

Purification


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earth potential. The present-day record is held by the tandem at Oak Ridge, which

operates with 24.5 MV on the high-voltage terminal, but a machine called Vivitron is

under construction at Strasburg with a design voltage of 35 MeV.


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6.VI VITRON in France

K-22 HCMUNS Dec.2012 47

1.3.4 World highest voltage for a static

accelerator VIVITRON in France

35 MV designbut operating voltage is 25 MV

DC-Accelerator

PART 1 LECTURE 1 page no HCMUNS 2013.pdf

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