Lecture 2 - Overview of Accelerators II ACCELERATOR PHYSICS MT 2004 E. J. N. Wilson

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ACINST2 - E. Wilson – 3-Oct-04 - Slide 1

Lecture 2 - Overview of Accelerators II

ACCELERATOR PHYSICS

MT 2004

E. J. N. Wilson

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Lecture 2 – Overview II- Contents

Strong focusing

CERN at BNL

CERN 25 GeV PS

Center of mass v. Fixed target

The first collider -AdA

ISR AND PS

Luminosity

SPS

Antiproton production and cooling

CERN Antiproton Accumulator

LEP

Superconducting magnets

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Weak focussing in a synchrotron

Vertical focussing comes from the curvature of the field lines when the field falls off with radius ( positive n-value)

Horizontal focussing from the curvature of the path

The negative field gradient defocuses

horizontally and must not be so strong as to cancel the path curvature effect

The Cosmotron magnet

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As the C magnet saturates the n value – which is the rate of droop – increases

The “n-value”

B

_z

= B

₀

1 − n Δr r

₀

⎛

⎝ ⎜ ⎞

⎠ ⎟ n = − r B

∂ B

∂ r f

_r

= f

₀

( 1 − n )

¹²

f

_z

= f

₀

n

¹²

Stable if : 0 < n < 1

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Cosmotron people

FOURGUYS.pct Christofilos - inventor E.Courant -Lattice Designer Stan Livingston - Boss

Snyder -theorist

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Strong focussing

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CERN at BNL

Odd Dahl, Frank Goward, and Rolf Widerö

(right hand trio)

Fig.3(CERNVISITORS).pct

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CERN 25 GeV PS

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Center of mass v. Fixed target

W = Energy available in center-of-mass for making new particles For fixed target :

E

_c.m.

≅ 2m

_T

E

_B

... and we rapidly run out of money trying to gain a factor 10 in c.m. energy

But a storage ring , colliding two beams, gives:

E

_{c .m.}

≅ 2 E

_B

Problem: Smaller probability that accelerated particles collide .... "Luminosity" of a collider

L = N

₁

N

₂

1 A

β c

2 π R ≈ 10

²⁹

...10

³⁴

cm

⁻²

s

⁻¹

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AdA - The first collider e-plus-minus

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ISR AND PS

ISR+PS.pct

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Imagine a blue particle colliding with a beam of cross section area - A

Probability of collision is

For N particles in both beams

Suppose they meet f times per second at the revolution frequency

Event rate

Luminosity

σ A ⋅ N

σ

A ⋅ N

²

f

_rev

= β c 2 π R f

_rev

N

²

A ⋅ σ

LUMINOSITY

Make small Make big

≈ 10

³⁰

to 10

³⁴

cm [

^-2

s

^-1

]

e. g. 10

⁻²⁵

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SPS

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Antiproton production and cooling

Protons at 26 GeV hit a target to produce pbars

3.5 GeV pbars are collected over as large a solid angel and energy spread as possible.

It takes 1.0 E12 protons to make 1.0E6 pbars.

We must inject and accumulate 1.0E5 pulses (about one day’s worth) but Liouville tells us we cannot.

Like pouring bromine into a funnel

SOLUTION IS TO CONDENSE

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TRANSVERSE COOLING

COOLPRINC.PCT

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Simple model of Stochastic Cooling (10 particles and a calculator)

At the pickup

“Maverick”

After kick

Maverick is nearer x=0 but this will not change next time unless we mix

After Mixing

Maverick will move in again

After many turns

of kicking and mixing

Center line

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STOCHASTIC COOLING ANALOGY

REST4.AD5

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CERN Antiproton Accumulator

AA.PCT

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LEP

LEP(small).pct

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Superconducting magnets

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