Superconducting Linacs: Why and How?

P N Prakash IUAC, New Delhi

IUAC

B.Sc. Summer Students Programme 2018

Inter University Accelerator Centre - June 14, 2018

Outline

• Introduction

• Van de Graff and Tandem Accelerator

• Quest for High Energies

• Superconducting Cavities & Linacs

• SC Linac Projects in India

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Charged Particle Acceleration

The Lorentz Force experienced by a charged particle:

F q E v B

W F.dl q (E v B).dl q E.dl q (v B).dl

Energy gained by the charged particle:

W q E.dl q (v B).vdtdl vdt,but so:

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Acceleration

In Particle Accelerators:

• Longitudinal electric fields are required for

accelerating charged particles.

• Magnetic fields are used for bending the

charged particle beams and for guidance

& focusing.

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Energy Gain

Output

Energy

Eout (> Ein)

charged

particle

beam

(p+, e-,

O6+, Ni8+

etc.)

Input

Energy

Ein

+

-

How is the energy of the beam increased ?

Energy Boosting

Device: Particle

Accelerator

EGain=Eout-Ein

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Accelerator - Example

A simple Particle Accelerator:

Energy gained by the electron:

EGain = q.V = 1x100 = 100 eV (electron volt)

Such DC - or static fields (voltages) - are used in Cockroft-

Walton generators and Van de Graff / Pelletron accelerators.

100 V

e- - +

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Cockroft Walton Generator IUAC

Cockroft Walton Generator (voltage multiplier).

Van de Graff Generator - Principle IUAC

0 0

1 q q q 1 1V(r) V(R)

4 r R 4 r R

since r < R; V(r) > V(R)

0

1 Q qV(R)

4 R R 0

1 Q qV(r)

4 R r&

Two conducting spheres

one inside the other.

Thus, charge on the outer sphere of radius R can be piled

up and the potential, can be increased to very

large values; at least until breakdown is reached. 0

1 QV(R) ,

4 R

irrespective of the value of “+Q”

When a conducting path is provided, charge will

flow from the inner sphere to the outer sphere !!

Van de Graff Generator IUAC

Left: Van de Graff Generator, and right: Van de Graff Accelerator at

Chalk River Laboratories, Canada.

Tandem Van de Graff IUAC

Ez Ez

The 15UD Pelletron Accelerator

at IUAC is a Tandem Accelerator.

z

15 UD Pelletron at IUAC IUAC

The Pelletron

Accelerator is

housed inside

the tower.

15 UD Pelletron at IUAC IUAC

Pelletron – Energy Gain

PelletronE 1.V q.V (1 q)V

ground to Terminal

(-ve ion) from Terminal to ground

(+ve ion with charge q)

0E E (1 q)V

Example:

Let: E0=200 keV (0.2 MeV), V=13 MV, q=10

E = 0.2 + (1+10)13 MeV

E = 143.2 MeV (1 MeV = 106 eV)

V

qV

E0

Pelletron Accelerator, such as

the one at IUAC, New Delhi.

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Start with a -ve Ion, strip it of electrons in

the Terminal and convert it into a +ve Ion.

Terminal

Quest for High Energies IUAC

High Energy Physicists

are looking for particle

beams of higher and

higher energies to

explore new physics

as close to t=0 (Big

Bang) as possible.

Nuclear Physicists

also look for high

energy heavy ion

beams above the

Coulomb barrier to

explore new physics.

Accelerators - Classification IUAC

ACCELERATORS

DC

(Van de Graff,

Tandem)

CYCLIC

(Cyclotron,

Synchrotron)

LINAC

(Room Temp.,

Superconducting)

DC Accelerators

Electrical breakdown (flash) is the major limitation in

going to higher Terminal Voltages (and therefore

achieving higher energies).

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The highest Terminal Voltage achievable is ~20 MV.

Increase in the Terminal Voltage means increase in the

size of the Outer Tank (that contains the insulating

gas).

Also, the Accelerator can only be vertical, since

sagging of the horizontal column is an issue. Going up

vertically, however, has its own limitations !!

Synchrotron IUAC

Synchrotron at

RRCAT, Indore.

Synchrotrons are not suitable for

accelerating electrons, unless the

accelerator is especially designed for

producing Synchrotron Radiation !!

4

1P

mRadiated Power

p

e

m2000

mremember,

Overcoming Limitations

• To increase the beam energy further, time-dependent

electric fields [rather than static (DC) electric fields]

have to be utilized.

• Such time-dependent electric fields are produced in

devices called CAVITY RESONATORS, which

operate at radio frequency (RF); typically around

hundreds of megahertz (MHz) frequency.

• A Linear Accelerator, or LINAC, uses a series of

cavities placed one after the other, to accelerate the

particle beam.

How to increase the beam energy further ?

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Acceleration in LINACS

In this representation, each

step indicates an RF Cavity

Resonator that boosts the

energy of the beam further.

In this way the energy of the beam can be increased

indefinitely by adding more and more Cavities.

#1

#2

#3

#4

#5

#6

Cavity Resonators

#1 #2 #3 #4 #(n-1) #n

Beam

Axis Ein Eout

EGain=Eout-Ein

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• A Linear Accelerator (LINAC) in which a series of Resonant Cavities

are installed one after the other to produce ion beams of high

energies, is called an “Independently Phased LINAC”.

• This is because each resonant cavity can be independently powered

and set up, so that when the beam bunch arrives at its entrance it

can accelerate it. This of course means that each cavity has its own

RF Amplifier and Control Module.

• Remember, as the beam gains energy, its speed changes !!!

Independently Phased LINAC

Independently Phased Resonators

#1 #2 #3 #4 #(n-1) #n

Beam

Axis Ein Eout

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ILC

The proposed International Linear Collider (ILC) will be a

500 GeV e--e+ collider. It will use 16,000 cavities placed in series

one after the other; the total length of which is 31 Km.

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A LINAC has the advantage, besides

being modular, of not losing beam

power due to radiation.

Cavities - Classification IUAC

Accelerating Cavity

Resonators operating in

TEM Mode. They are

used for accelerating

particles moving at

slower speeds (<0.5c).

They are cylindrical in

shape with one or more

central elements.

Cavities operating in TM

Mode. They are used for

accelerating particles

moving at high speeds

(>0.5c). They are usually

Elliptical in shape, with

several cells in a single

structure.

How do TM Class cavities look?

RF

Power In

Beam Induced

Power Out βλ/2

The ILC requires 16,000 such 9-cell

Superconducting Niobium Cavities !!

βλ/2

Single Cell Cavity

Transverse Magnetic, or TM-Class Elliptical Cavities, are used for particle

acceleration in e--e+ Colliders and high energy sections of H+ LINACS.

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How do TEM Class cavities look?

Transverse Electric & Magnetic, or TEM-Class Resonators, are

used for accelerating heavy ions which move at slow speeds.

/4 E

H

Quarter Wave Resonator

E ℓ= /2

H

H

Beam

Axis

Half Wave Resonator

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How does a Resonant Cavity work ??

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Standing Wave

Standing waves produced on a string.

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In a Resonant Cavity

such Standing Waves

are produced.

However, the waves in

a Cavity are

Electromagnetic !!!

Pill-Box Cavity – TMnpj Mode

Electric and magnetic fields in the pill-box

cavity in the TM010 mode.

Jn(x) as a function of x.

z n c,np jE J (k r)cos(n )cos(k z)exp(i t)

zH 0

j 'r n c,np j

c,np

kE J (k r)cos(n )sin(k z)exp(i t)

k

j

n c,np j2c,np

k nE J (k r)sin(n )sin(k z)exp(i t)

k r

0r n c,np j

c,np

i nH J (k r)sin(n )cos(k z)exp(i t)

k r

'0n c,np j

c,np

iH J (k r)cos(n )cos(k z)exp(i t)

k

The general solution of the time

dependent fields in TMnpj modes is

given by:

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Pill Box

Cavity

b

H

E

TEM Class Resonant Cavity

Consider a Co-axial Cylinder having conducting walls:

Beam

Axis

Attach Beam Ports so that the

structure becomes useful for

acceleration.

Such a structure is called a Transverse Electric-Magnetic, or

TEM-Class Coaxial Cavity Resonator.

Introduce a conductive “loading element” and attach it to the cavity

with conducting end caps.

when , or

transverse electric-magnetic standing

wave modes can exist in the cavity.

ℓ

2 2

n

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Coaxial Resonator

x

y

z

r

θ

Imagine a current wave on the inner conductor traveling

in the +z direction:

0I I exp j( t kz)

This current produces an azimuthal

magnetic field:

0 0B I 2 r exp j( t kz)

The radial electric field Er will be:

r 0 0E I c 2 r exp j( t kz)

Coaxial Resonator

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Coaxial Resonator

x

y

z

r

θ

Similarly, a current wave traveling in the -z direction is

given by:

0I I exp j( t kz)

This current will produce an

azimuthal magnetic field:

0 0B I 2 r exp j( t kz)

The radial electric field Er is:

r 0 0E I c 2 r exp j( t kz)

Coaxial Resonator

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Coaxial Resonator

The waves traveling in the +z and –z directions add to produce

a standing wave satisfying the boundary condition Er = 0 at z=0

and z=ℓ.

z=ℓ

Coaxial Resonator

x

y

z

r

θ

z=0 ℓ

0 0IB cos p z exp j( t)r

The non-zero field components are:

0 0r

0

IE 2j sin p z exp j( t)

2 r

z

p ck c ,p 1,2,3........where,

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Coaxial Resonator

0 0r

0

IE 2j sin p z exp j( t)

2 rRadial electric field:

we know: j exp j 2 .

0 0r

0

IE 2 sin p z exp j( t 2)

2 r

Bθ

A

A

N

Er

N N

A

This shows that the Electric and

Magnetic standing waves have a

phase difference of π/2 between them.

Er

Beam Ports are

attached where

Er is maximum.

The electromagnetic energy

oscillates between the electric

and magnetic fields.

0 0IB cos p z exp j( t)r

azimuthal magnetic field:

&

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How do ions gain energy ?

E E

d2

Beam

Axis

Coaxial Resonator

E

H

( v c)

H

E

+ve ion

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Accelerating Module

The inside of a LINAC Cryomodule which has eight Quarter Wave Resonators installed

one after the other. This picture is from the Superconducting LINAC at IUAC.

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Accelerating Gradient

The longitudinal Electric Field Ez experienced by a

charged particle in the cavity resonator is averaged

over the effective length over which the accelerating

electric field extends.

Ea is the average accelerating gradient (or field, if

you like), in the cavity which extends over the

effective length, Leff .

z a effE dz E L

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Accelerating Gradient

Gain z a effW E q E dz qE L

Much of the R&D in the field of Linear Accelerators is

therefore devoted towards producing and maximizing

the accelerating gradient Ea, for a given amount of

input power.

Energy gained by a particle having charge q:

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Enter Superconductivity !!!

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Superconductivity

• Microwave surface resistance of high conductivity materials:

• Cu at 300 K @ 100 MHz frequency, Rs ~3 mΩ

• Nb at 4.2 K @ 100 MHz frequency, Rs ~10 nΩ

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Energy stored Energy stored UQ=2 2 f

Energy dissipated per cycle Power dissipated P

The efficiency with which an accelerating structure stores

(or retains) the energy is given by the figure of merit

“Quality Factor”, usually denoted by Q (or Q0).

where ω is the angular frequency, U is the stored energy in

the cavity and P is the power dissipated in the cavity walls.

Superconductivity

The most striking features of a superconducting resonator

are the accelerating electric field Ea and the quality factor Q.

• High accelerating fields achieved in superconducting

resonators make the accelerator compact.

• High quality factor reduces the total power required to

produce / generate those fields.

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s 5Cu

s Nb

R10

R5Nb

Cu

Q10

QQ~109 versus 104

Superconductivity

Normal

Conducting Superconducting

Frequency (MHz) 100 100

Stored Energy (J/(MV/m)2) 0.1 0.1

Quality Factor (typical) 1 104 2 108

Accelerating Field (MV/m) 3 3

Power dissipated (W) 56,000 3

The superconducting resonator reduces the required wall plug power by

a factor of >100, which is very-very significant !!

Comparison between a resonator made from normal conducting material

(e.g. copper) and superconducting material (e.g. niobium):

Carnot

4.20.014

300 4.2

Refrigerator Efficiency ~0.2

Net Efficiency ~0.003

Wall Plug Power ~1 KW

Superconducting:

RF Source Efficiency ~0.5

Wall Plug Power ~112 KW

Normal Conducting:

AC Power required 112 KW 1 KW

higher than actual !! lower than actual !!

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Clearly, superconducting accelerating structures

have advantage over room temperature structures

in terms of the wall plug power required.

However, they have their set of issues.

Life is never easy !!

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Issues with SC Cavities

Superconducting Niobium Cavities are non-trivial to develop:

• They need to be designed to maximize the gradient

without reaching the fundamental limit of the critical

magnetic field (most important among the limits).

• They need to be designed to operate at low temperatures

(4K, or 2K in some cases).

• They require special infrastructure to construct.

• Niobium is an expensive material US$750-1000/Kg);

each cavity typically requires 10s of kilograms of material.

• Constructing a Superconducting Cavity is a finicky and

risky process.

• Diagnosing problems in Superconducting Cavities can

become very tricky.

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Developments at IUAC

Superconducting Niobium Cavity development at IUAC:

• IUAC is the first laboratory in India to set up the necessary

infrastructure to indigenously build Superconducting

Niobium Resonant Cavities.

• Two thirds of the SC Resonators used in the IUAC Linac

are built indigenously using this infrastructure.

• IUAC has also collaborated with several Indian

Laboratories to develop niobium cavities of different

designs.

• IUAC has collaborated with Fermi National Accelerator

Laboratory to develop Single Spoke Resonators for a

project (details in later slide).

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Superconducting Booster LINAC

Quarter Wave Resonator

(QWR) used in IUAC Linac.

15 UD Tandem Pelletron Accelerator &

Superconducting Linear Accelerator (SC LINAC)

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Indigenously Developed QWRs

IUAC QWR

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SC LINAC at IUAC IUAC

Fermilab PIP-II & Indian Programs

HWR SSR1 SSR2 Elliptical Cavities

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• Proposed High Intensity Superconducting Proton

Accelerators in India (ISNS, ADS)

- Accelerators similar to PIP-II

- Overlapping Technologies

Accelerator Development - BARC, RRCAT, IUAC & VECC

Indian Institutions and Fermilab Collaboration (IIFC)

Proton Improvement Plan (PIP-II) at Fermilab, USA.

Spoke Resonator - SSR1

The two SSR1 Niobium Spoke Resonators developed at IUAC.

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IUAC SSR1 S104 Test Result

2 K Test Result of SSR1 S104 developed at IUAC and tested at Fermilab. The

PIP-II and PXIE Design Goals are Eacc=10 & 12 MV/m respectively at Q>5 109.

IUAC SSR1 S104

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There are several other developments but it is

beyond the scope (and time) for this lecture…..

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Thank you

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