Introduction to particle accelerators and their applications - Parte II: Components

Introduction to particle

accelerators and their applications - Parte II:

Components

Gabriele Chiodini

Istituto Nazionale di Fisica Nucleare

Sezione di Lecce

PhD lessons in Physics for Università del Salento

2015-16 (20 hours, 4 CFD)

The component of an accelerator

• ^Source

• Injection (non treated here)

• ^Vacuum

• ^Magnets

• ^RF

• Extraction (non treated here)

Source

Electrons

Thermionic emission Photoemission

Ions

ECR

Penning (PIG)

Negative Ions

Electron sources

• ^Vacuum

• Electrons emitted by a cathode

• An anode with or without a hole

• Acceleration potential

• Focusing structure

Thermionic emission

Metals heated to temperatures close to incandescence emit

Photoemission

Planck constant h=6.6E-34 J x s = 4.1E-15eV x s

The electrons of a metal can receive higher energy than vacuum energy absorbing photons ( photocathode and laser)

Metals QE=0.01% !

Semiconductor QE ~=10-30%

The accelerating structure is a RF cavity

QE=Quantum efficiency=N electrons/N photons

Quantum efficiency

QE is determined by a three step process:

!

1. Electron excitation from the valence band to conductive band

2. Electron-phonon and electron-electron scattering thermalise the electron approaching the surface

3. The electron affinity with respect to the conduction band minimum determine the probability of emission in vacuum of electron in conduction band and near the surface

! • Step 2 and 3 is less favorevol for metal than semiconductor.

• The semiconductor photocathode have high QE but low

stability in time.

Ions source

• Gas inlet

• Ionizing power input

• Plasma production region

• Magnetic confinement

• Ions extractions

Plasma

The 4th state of matter:

the plasma

• It is a rarefied and ionized gas electrically neutral (molecules, ions+, ions-, electrons).

• It screens electrically a charged object placed inside by the formation of a charge layer

• It is created by heating,

electric discharge, microwave

absorption, laser absorption

Charged particle motion in a plasma

1. Cyclotron motion along B.

Radius of tens of micron for electrons and few millimetre for ions.

2. Drift motion orthogonal to E and B equals for electrons and ions (no charge, no mass dependence).

3. Magnetic mirror or bottle (not homogeneous B push charged particles versus low field region).

ρ

= qB mv

v

= E

B

1

2

3

ECR (Electron Cyclotron Resonace) ion source

f

(elettroni) = v

2 πρ ⁼ 1 2 π

eB m

f

(elettroni) = 28B(T) = f

(GHz) condizione di risonananza ECR

• The ECR plasma production region ( discharge region ) corresponds to the region where the electron cyclotron frequency is equal to the frequency of the input microwave ( resonance).

• The electrons are trapped by the magnetic mirror and heats up to keV and even to MeV energy level.

• The ions slip-out the magnetic mirror because heavier than electrons, and form the ion beam.

• No thermionic filament is used and then it is a very robust source.

ECR resonance condition

real ECR

Penning ion source or 


Philips Ionization Gauge(PIG)

• Pressure = 1E-3 Atm

• ^{B=0.1 T}

• Hot or cold cathode

• Electrons are accelerated in arc discharge due to the high voltage between anode and cathode (V=1kV and I=0.1-50A )

• Electrons rotate around B (tens of micron radius) and ionise the gas very effectively before to reach the anode.

• The ions slip-out from the hole and form the

ion beam.

Real PIG real

Negative ion source

The negative ions are generated from positive ions or neutral atoms by electron transfer from substance with low electron affinity, such as an alkali metal ( for example cesium ).

Electron affinity = Energy released from electron transfer

B

Production and extraction of negative ions

NEGATIVE ION EXTRACTION

• The extraction of negative ions favours also the extraction of electrons because they have the same charge .

• By means of a dipole you can separate the electron current from the negative ion beam.

Technique 1: caesium coated cathode (surface phenomena)

Technique 2: gas+caesium

mixture(bulk phenomena)

Vacuum systems

Pressure units

The vacuum is a force: Pressure x Surface

P = nkT

Gas law n[molecules/m3]=molecular density

!

Boltzman's constant k=1.38E-23 J/K = 8.6E-5eV/K

Mass flow and Throughput

!

The quantity of gas flowing through a piping element is described by:

• Mass Flow=Mass/Time (Kg/s)

• Throughput Q = pV/Time (mbar x litre / s ) . NB 1: In a perfect gas pV=M/mkT

NB 2: The outgassing is measured in mbar x litre /s like Q

C[litres/s]=Conductance

Q=Throughput [litre x mbar / s] P1-P2=pressure drop[mbar]

Conductances in parallel increase

Conductances in series decrease C(hole area A )=11.6A[cm

] C(tube of diameter D and length L )


=12.1D

/L[cm

]

It is better short and large tubes

Effective pumping speed

The pumping speed is limited by the conductance of the connecting pipe:

Example: a turbo molecular pump of 8 keuro have a pumping speed S=400 l/s.

If I connect a pipe of diameter d=10 cm and length L=2m I have C=60l/s then S

~60l/s.

Pumping speed of a pump

Pumping time

Q = S x p

Vdp/dt = S x p dp/dt = S x p / V dp/dt/p=S/V

In a vacuum tight volume V at pressure p without gas leak the pumping time is determined by the

where S is the effective pumping speed

The pressure follow the exponential decay law with time

constant = S/V

Viscous and molecular flow

λ

[cm] ~ 6.7 ⋅10

P[mbar]

1 < P < 10

mbar 6.7 ⋅10

< λ

< 6.7 ⋅10

cm

10

< P < 1 mbar ^{6.7 ⋅10}

^{< λ}

< 6.7 cm

P < 10

mbar 6.7 cm < λ

Molecular flux: dominated by collisions with the wall Viscous flux: dominated by intra-molecule collisions Molecular mean free path in air

• The two regimes differ each other completely for calculations and vacuum components.

• The molecular regime is the true vacuum technology and is dominated by the nature of the surface

walls which continuously release molecules ( Outgassing )

Vacuum classification

• Medium vacuum: 10 ^-3 <P<1mbar 


viscous flux

• High vacuum: 10 ^-7 <P<10 ^-3 mbar 


molecular flux

• Ultra high vaccum: 10 ^-12 <P<10 ^-7 mbar 


molecular flux

Outgassing and cleaning

• In a vacuum system the final pressure is given by the OUTGASSING of the surface walls.

• The outgassing depends on the nature, treatment, cleaning, temperature and pumping time

• Methods of cleaning

• Remove residues by chemical products

• Fire under vacuum at 9500C to extract hydrogen from stainless steel

• Electrical discharges to remove gas and atomic metal

• Heating to 1500C to remove water molecules ( bake- out )

P _finale = Q outgas sin g

S _eff

Use ONLY metals NEVER plastics:

Q plastics =5000Q metals

Metals vs Plastics

P

= Q

S

= q

A

S

Vacuum measurements 1:

1E-4mbar<P<1 mbar

PIRANI GAUGE

below 1E-4mbar gives wrong values The reading is done by zeroing a resistive bridge by

setting the current value necessary to maintain constant

the temperature of a THERMISTOR placed in vacuum .

Lower is the pressure, less cooling on the thermistor

and less current is needed to keep it warm.

Vacuum measurements 2:

1E-10mbar<P<1E-5 mbar

PENNING GAUGE

M e a s u r e t h e

discharge current of

a P e n n i n g c e l l

b e t w e e n c o l d

cathode and cold

anode in magnetic

field.

Vacuum measurements 3:

1E-12mbar<P<1E-5 mbar

BAYARD-ALPERT GAUGE

Measure the current of the electrons emitted in

vacuum from a hot filament and rotating in a

magnetic field

Pumps to create the vacuum

Primary rotational pump ( dry or oil ) used to pump from environmental pressure to 1E - 2 mbar . S = m3 / h .

It works in viscous regime creating a pressure drop between input and output .

Often it prepares the vacuum for the turbomolecular pump.

Pumps to create the vacuum

Turbo-molecular pump used to pump from 1E-2 mbar up to 1E-11mbar and then it can be removed. S = 10 to 3000 l / s .

It works in molecular regime by

momentum transfer: when a

molecule touches the blades

rotating at a very high speed

comparable to the molecule

thermal speed the molecule is

removed from the volume .

Pumps to keep the vacuum

!

Ion sputtering pump is used to maintain the vacuum and can work from 1E- 5 mbar up to 1E-11mbar. S = 1-500 l/s .

It is a Penning cell where the emitted electrons ( 6kV ) ionize residual molecules and sputter the titanium covering the cathode.

The sputtered titanium can

chemically bond the residual

gases or bury the not reactive

o n e ( n o b l e g a s e s a n d

hydrocarbons ) carrying them

on the metal walls where they

Vacuum components

Below

Cooper pipe

Collar,gasket, L-pipe Flange

Secti on va lves

Normal conductive

magnets

Magnet components

Normal conductive magnet

• ^{PRO IRON}

• Less Ampere x Nturn

• Less dissipated power

• Guide and shape the magnetic field

• CONV IRON

• Saturate at about 2 Tesla (all magnetic domains are oriented along B)

B

= µ

^NI

h = B

(1 + χ

⁾

Microscopic currents (oriented magnetic domain)

The standard coil is made by rectangular wires of copper or Coil

aluminium with cooling water going through.

The wires are isolated and glued together by glass and epoxy resin.

2 Layers

4 Layers

• Maximise NI (Ampere x turn)

• Choose conductor area A and number of turn N

• Current density J= NI/A

Many N: low current (less losses), small terminal (easy and cheap connection), more isolation, more assembly cost, higher voltage

Low J : less losses, less consumption, less cooling

The limit of the normal conductive magnets

The iron saturates at T = 1.5 -1.8T and in ramping regime as in a synchrotrons can not exceed a magnetic field of 1-1.2T .

!

You need to switch to the superconducting magnets (zero electric resistance) which are free of iron, but just coils with very high currents (10,000 A) and no power dissipation.

!

But the superconductive magnet coil must be kept at

temperatures close to absolute zero and therefore require

cryogenics cooling systems.

Comparison normal and super conductive magnets

T=4.2K At LHC (Large Hadron Collider) all the magnets are made of NbTi superconductive and cooled

down to less than 2 K.

!

The cryogenic fluid at LHC is the superfluid He II (PERFECT HEAT CONDUCTOR):

• zero viscosity

• second sound (heat waves)

Radio-Frequency

accelerating structure

What is a RF system

• A charged particle could be accelerated only electric field parallel to the direction of motion

• Variable fields can increase energy without voltage built-up

• Wideroe’s drift tube can work only at low frequency because at high frequency the drift tube are not anymoe equipotential:

• low energy

• low filed gradient

It is necessary to abandon drift tubes with uniform fields

for accelerating structures with distributed fields

Electromagnetic

spectrum

Dispersion relation in a pipe

Vacuum Cylindrical


pipe

Waveguide

Dispersion relation in a RF cavity

RF cavity

Waveguide with

obstacles

Main RF components

• RF oscillator

• RF power amplifier

• Coupling amplifier-cavity

• Accelerating cavity

• IN and OUT beam

• IN and OUT RF wave

• Power meter (Antenna)

Disk-loaded guide waves with traveling waves (TW)

Guide wave IRIS-loaded:

• f=2.856 GHz (S band)

• 86 acceleration cells

• Coupling input/output

• Accelerating file 30 MV/m

Wave guide allows to create a

longitudinal component to the

electromagnetic field and the

discs to reduce the wave

phase velocity less than the

velocity of light in vacuum in

such a way it can accelerate

RF resonator with standing wave (SW)

Reentrant Nose-cone Disk-loaded Coaxial

The resonant cavities are characterised by stationary resonant modes that oscillate in time with frequency f and in the space with a wavelength λ without propagate ( Standing Wave ) . The standing wave is the sum of two waves traveling in the opposite direction and completely interfering at the boundaries.

V

(x, t) = V

sin(2πft − 2π λ x) V

(x, t) = V

sin(2πft)sin( 2π λ x)

Traveling wave Standing wave

The boundary conditions

decide if TW o SW

Figure of merit of a RF cavity

• E=Accelerating field =V/L (Inside the Cavity)

• Q=Total Energy/ Dissipated Energy =U/P=f

/Δf

• Dissipated energy P due to surface resistivity of the RF conductor wall at high frequency (skin effect) = V x I = V

/R = I

R (In Cavity Wall).


R can be drastically reduce by a super-conducing RF cavity (Rs=8nΩ one million time lower than

0

The penetration of an alternating current is not complete in a c o n d u c t o r c r o s s section due to the

“Skin Effect”

RF oscillator

• A transistor is a current amplifier

• The output signal is in opposite phase with the input ( inverting )

• Two inverting stages are not inverting

• Sending at the input a fraction of the output signal triggers a positive feedback loop with frequency f

=1/(RC).

Feed-back:

• Positive=self sustained oscillation

• Negative=stable gain amplifier

R C

RF solid state amplifiers

Many amplifiers in parallel:

• f=325 MHz

• ^{P=190 kW}

• 4.7x4.7x2.3m3

Tetrode as RF power

amplifier _• In thermionic valves the conduction of current is possible only for electrons emitted from the hot cathode and collected by the anode (diode) .

• In the triode the control grid modulates the passage of the electrons between the cathode and the anode amplifying the signal of the grid on the anode.

• In a tetrode a constant potential grid shields the control grid from the anode an reduce the electric capacitance between control grid and anode allowing to work at higher frequency than a triode.

• The frequency limit is due to the transit time of the electrons from cathode to anode which can not reduced too much reducing the distance

Tetrodo

Klystron

Speed

modulation Position modulation

(bunches)

• The klystron works on the principle of speed modulation

• An electron gun generates an electron beam .

• The gap1 ( Buncher ) is fed by a RF wave at high frequency

• Electrons arriving in Gap 1 are accelerated differently depending on the location ( speed modulation) and continue towards the Gap 2 ( Catcher )

• The faster electrons arrive in GAP2 in advance and the slower ones are late ( position modulation)

• In GAP2 the electrons travel in dense bunches and emit an intense

electromagnetic wave at the output

Real Klystrons