eric prebys fnal accelerator physics center june 7-17, 2010

Eric Prebys

FNAL Accelerator Physics Center

June 7-17, 2010

History and movitation for accelerators Basic accelerator physics concepts Overview of major accelerators

emphasis on LHC Other uses for accelerators The future

Crazy ideas

2Eric Prebys, "Particle Accelerators", QuarkNet Summer Institute at NIU June 7-17, 2010

The first “particle physics experiment” told Ernest Rutherford the structure of the atom (1911)

In this case, the “accelerator” was a naturally decaying 235U nucleus

The first artificial acceleration of particles was done using “Crookes tubes”, in the latter half of the 19th century These were used to produce the first X-rays (1875)

Study the way radioactive particles “scatter” off of atoms


To probe smaller scales, we must go to higher energy

To discover new particles, we need enough energy available to create them

The rarer a process is, the more collisions (luminosity) we need to observe it.

GeV/cin

fm 2.1

pp

h

2mcE


1 fm = 10-15 m(Roughly the size of a proton)

Accelerators allow us to probe down to a few picoseconds after the Big Bang!5Eric Prebys, "Particle Accelerators", QuarkNet Summer Institute at NIU June 7-17, 2010

Radioactive sources produce maximum energies of a few million electron volts (MeV)

Cosmic rays reach energies of ~1,000,000,000 x LHC but the rates are too low to be useful as a study tool Remember what I said about

luminosity! On the other hand, low

energy cosmic rays are extremely useful But that’s another talk

Max LHC energy


eeThe simplest accelerators

accelerate charged particles through a static electric field. Example: vacuum tubes (or CRT TV’s)

eV

eVeEdK Cathode Anode

Limited by magnitude of static field:

- TV Picture tube ~keV- X-ray tube ~10’s of keV- Van de Graaf ~MeV’s

Solutions:

-Alternate fields to keep particles in accelerating fields -> RF acceleration-Bend particles so they see the same accelerating field over and over -> cyclotrons, synchrotrons

7

FNAL Cockroft-Walton = 750 kV

)(tV

tNominal Energy

Particles with lower E arrive later and see

greater V.

)(tV

tNominal Energy

Particles with lower E arrive earlier and see greater V.

Particles are typically accelerated by radiofrequency (“RF”) electric fields. Stability depends on particle arrival time relative to RF phase “bunched” beams

If velocity dominates If momentum (path length) dominates


“bunch”

Fermilab Drift Tube Linac (200MHz): oscillating field uniform along length

ILC prototype elipical cell “-cavity” (1.3 GHz): field alternates with each cell

JLab compact “toaster cavity” (400MHz): low frequency in a limited space


1930 (Berkeley) Lawrence and

Livingston K=80KeV

1935 - 60” Cyclotron Lawrence, et al.

(LBL) ~19 MeV (D2) Prototype for many


60” cyclotron (1935) Berkeley and elsewhere

Fermilab Radius = 1km Built ~1970 Upgraded ~1985, ~1997 Until recently, the most

powerful accelerator in the world.


Tunnel originally dug for LEP Built in 1980’s as an electron positron collider Max 100 GeV/beam, but 27 km in circumference!!

Now we’ll talk a little about how these things work…

/LHC

My House (1990-1992)


The next few slides contain a lot of mathematical detail.

They’re not meant to be fully absorbed real time by everyone.

I’ll follow them with a “glossary”, which will qualitatively summarize the key concepts.

June 7-17, 2010Eric Prebys, "Particle Accelerators", QuarkNet Summer Institute at NIU 13

A charged particle in a uniform magnetic field will follow a circular path or radius

Typical Magnet Strength Conventional: ~1 T Latest superconducting: ~8T Next generation superconducting

(Nb3Sn): ~15T

]T[

300/]MeV/c[]m[

p

B

p

eB

side view

B

top view“Thin lens” approximation:

If the extent of the magnetic field is short compared to , then the particle experience and angular “kick”

p

BL

14

p

l

B p

B

Vertical Plane:

Horizontal Plane:

Luckily…

…pairs give net focusing in both planes! -> “FODO cell”


xB

y

yB

x

)(sin)()( 2/1 ssAsx

s

s

dss

0 )()(

For a particular particle, the deviation from an idea orbit will undergo “pseudo-harmonic” oscillation as a function of the path along the orbit:

The “betatron function” s is effectively the local wavenumber and also defines the beam envelope.

Phase advance

Lateral deviation in one plane

Closely spaced strong quads -> small -> small aperture, lots of wiggles

Sparsely spaced weak quads -> large -> large aperture, few wiggles

s

x


Generally, we don’t want the tune in either plane or their combination to be a low order rational number

As particles go around a ring, they will oscillate around the ideal orbit a fixed number of times. This number is called the “tune” (usually or Q)

Ideal orbit

Particle trajectory

6.7Integer :

magnet/aperture optimization

Fraction: Beam Stability

y)instabilit(resonant mkk yyxx

“small” integersfract. part of X tune

frac

t. pa

rt o

f Y tu

ne17Eric Prebys, "Particle Accelerators", QuarkNet Summer Institute at NIU June 7-17, 2010

22 ''2 xxxx TTT

x

'xAs a particle returns to the same point on subsequent revolutions, it will map out an ellipse in phase space, defined by

Area =

Twiss Parameters

An ensemble of particles will have a “bounding” . This is referred to as the “emmitance” of the ensemble. Various definitions:

T

x

2

T

x

26

Electron machines:

Contains 39% of Gaussian particles

Proton machines:Contains 95% of Gaussian particles

Usually leave as a unit, e.g. E=12 -mm-mrad

(FNAL)


00

0

0 N

)(

)(s

sx T

As the beam accelerates “adiabatic damping” will reduce the emittance as:

so we define the “normalized emittance” as:

The usual relativistic and

We can calculate the size of the beam at any time and position as:

Plane [-mm-mrad] [m] Injection ExtractionHorz 12 33.7 19.9 6.5Horz 12 6.1 8.5 2.8Vert 12 20.5 15.5 5.1Vert 12 5.3 7.9 2.6

beam size [mm] (95%)

Example: Fermilab Booster

2

*

1

1 ;

c

v


When a particle hits another particle, the probability that a particular reaction will occur has units of area Think about the probability of hitting a window while randomly throwing balls at a wall. This is referred to as “cross-section”

The higher the cross-section, the more probable an interaction For historical reasons, we often use the unit of “barn”, where

1 barn 1x10-24 cm2 total nuclear cross-section

The processes we are interested in today are generally measured in small fractions of a “barn” picobarn (pb), femtobarn (fb), etc.


tNLtNR nn

The relationship of the beam to the rate of observed physics processes is given by the “Luminosity”

Rate

Cross-section (“physics”)“Luminosit

y”Standard unit for Luminosity is cm-

2s-1

For fixed (thin) target:

Incident rateTarget number density

Target thickness Example: MiniBooNe primary target:

1-237 scm 10 L

LR

21

21 NA

N

Circulating beams typically “bunched”

(number of interactions)

Cross-sectional area of beamTotal Luminosity:

C

cn

A

NNr

A

NNL b

2121

Circumference of machineNumber of

bunches

Record e+e- Luminosity (KEK-B): 1.71E34 cm-2s-1

Record Hadronic Luminosity (Tevatron): 4.03E32 cm-2s-1

LHC Design Luminosity: 1.71E34 cm-2s-122Eric Prebys, "Particle Accelerators", QuarkNet Summer Institute at NIU June 7-17, 2010

The total number of interactions is given by the cross-section times the integral of the luminosity over time:

The integrated luminosity has units of cm-2, but for historical reasons it is almost always quoted in “inverse barns” (or more often “inverse picobarns” (pb-1), “inverse femtobarns” (fb-1), etc) 1 b-1 = 1024 cm-2

1 fb-1 = 1039 cm-2

The integrated luminosity is the ultimate measure of “what an accelerator has delivered”.

Example: the Fermilab Tevatron has delivered roughly 7 fb-1 of proton-antiproton collisions per experiment, so something with a 10 fb cross-section would have produced 7x10=70 events by now.


L LdtN

“RF cavity”: resonant electromagnetic structure, used to accelerate or deflect the beam.

“Bunch”: a cluster of particles which is stable with respect to the accelerating RF

“Dipole”: magnet with a uniform magnetic field, used to bend particles “Quadrupole”: magnet with a field that is ~linear near the center, used to

focus particles “Lattice”: the magnetic configuration of a ring or beam line “Beta function ()”: a function of the beam lattice used to characterize the

beam size. “Emittance ()”: a measure of the spacial and angular spread of the beam

“Tune”: number of times the beam “wiggles” when it goes around a ring. Fractional part related to beam stability.

“Cross-section”: a measure of how likely a reaction is to occur. “Luminosity”: a measure of the rate at which “particles hit each other”.

You need a high luminosity to observe a rare process. “Integrated Luminosity”: luminosity x time, the “bottom line” as to what

an accelerator has delivered.

T beam of size


How were the choices made? Colliding beams vs. fixed target Protons vs. electrons Proton-proton vs. proton anti-proton Superconducting magnets Energy and Luminosity

25June 7-17, 2010Eric Prebys, "Particle Accelerators", QuarkNet Summer Institute at NIU

For a relativistic beam hitting a fixed target, the center of mass energy is:

On the other hand, for colliding beams (of equal mass and energy):

2targetbeamCM 2 cmEE

beamCM 2EE

To get the 14 TeV CM design energy of the LHC with a single beam on a fixed target would require that beam to have an energy of 100,000 TeV! Would require a ring 10 times the diameter of

the Earth!!

26

Electrons are point-like Well-defined initial state Full energy available to

interaction Can calculate from first principles Can use energy/momentum

conservation to find “invisible” particles. Protons are made of quarks and gluons

Interaction take place between these consituents.

At high energies, virtual “sea” particles dominate

Only a small fraction of energy available, not well-defined.

Rest of particle fragments -> big mess!

So why don’t we stick to electrons??27Eric Prebys, "Particle Accelerators", QuarkNet Summer Institute at NIU June 7-17, 2010

As the trajectory of a charged particle is deflected, it emits “synchrotron radiation”

4

2

2

06

1

m

EceP

An electron will radiate about 1013 times more power than a proton of the same energy!!!!

• Protons: Synchrotron radiation does not affect kinematics very much

• Electrons: Beyond a few MeV, synchrotron radiation becomes very important, and by a few GeV, it dominates kinematics - Good Effects: - Naturally “cools” beam in all dimensions - Basis for light sources, FEL’s, etc. - Bad Effects: - Beam pipe heating - Exacerbates beam-beam effects - Energy loss ultimately limits circular accelerators

Radius of curvature


Proton accelerators Synchrotron radiation not an issue to first order Energy limited by the maximum feasible size and magnetic

field. Electron accelerators

Recall

To keep power loss constant, radius must go up as the square of the energy (weak magnets, BIG rings): The LHC tunnel was built for LEP, and e+e- collider which

used the 27 km tunnel to contain 100 GeV beams (1/70th of the LHC energy!!)

Beyond LEP energy, circular synchrotrons have no advantage for e+e-

-> International Linear Collider (but that’s another talk)

224

2

2

06

1

E

m

EceP


Beyond a few hundred GeV, most interactions take place between gluons and/or virtual “sea” quarks. No real difference between proton-antiproton and proton-proton

Because of the symmetry properties of the magnetic field, a particle going in one direction will behave exactly the same as an antiparticle going in the other direction Can put protons and antiprotons in the same ring

This is how the SppS (CERN) and the Tevatron (Fermilab) have done it.

The problem is that antiprotons are hard to make Can get ~2 positrons for every electron on a production target Can only get about 1 antiproton for every 50,000 protons on

target! Takes a day to make enough antiprotons for a “store” in the

Fermilab Tevatron Ultimately, the luminosity is limited by the antiproton current.

Thus, the LHC was designed as a proton-proton collider.


For a proton accelerator, we want the most powerful magnets we can get

Conventional electromagnets are limited by the resistivity of the conductor (usually copper)

The field of high duty factor conventional magnets is limited to about 1 Tesla An LHC made out of such magnets would be 40 miles in

diameter – approximately the size of Rhode Island. The highest energy accelerators are only possible

because of superconducting magnet technology.

22 BRIP Power lost Square of the field


Conventional magnets operate at room temperature. The cooling required to dissipate heat is usually provided by fairly simple low conductivity water (LCW) heat exchange systems.

Superconducting magnets must be immersed in liquid (or superfluid) He, which requires complex infrastructure and cryostats

Any magnet represents stored energy

In a conventional magnet, this is dissipated during operation.

In a superconducting magnet, you have to worry about where it goes, particularly when something goes wrong.

dVBLIE 22

2

1

2

1


Tc

Superconductor can change phase back to normal conductor by crossing the “critical surface”

When this happens, the conductor heats quickly, causing the surrounding conductor to go normal and dumping lots of heat into the liquid Helium This is known as a “quench”.

Can push the B field (current) too high

Can increase the temp, through heat leaks, deposited energy or mechanical deformation


*pulled off the web. We recover our Helium.


W (MW=80 GeV)

Z (MZ=91 GeV)

The rate of physical processes depends strongly on energy For some of the most

interesting searches, the rate at the LHC will be 10-100 times the rate at the Tevatron.

Nevertheless, still need about 30 times the luminosity of the Tevatron to study the most important physics


Parameter Tevatron “nominal” LHC

Circumference 6.28 km (2*PI) 27 km

Beam Energy 980 GeV 7 TeV

Number of bunches 36 2808

Protons/bunch 275x109 115x109

pBar/bunch 80x109 -

Stored beam energy 1.6 + .5 MJ 366+366 MJ*

Initial luminosity 3.3x1032 (cm-2s-1) 1.0x1034(cm-2s-1)

Main Dipoles 780 1232

Bend Field 4.2 T 8.3 T

Main Quadrupoles ~200 ~600

Operating temperature 4.2 K (liquid He) 1.9K (superfluid He)*2 MJ ~ “stick of dynamite” -> Very scary


Even with the higher rates, still need a lot of interactions to reach the discovery potential of the LHC


100 fb-1/yrS

HU

TD

OW

N1000 fb-1/yr

200

fb

-1/y

r

3000

300

30

10-20 fb-1/yr

SUSY@3TeVZ’@6TeV

SUSY@1TeV

ADD X-dim@9TeV

Compositeness@40TeV

H(120GeV)

Higgs@200GeV

50 x Tevatron luminosity

500 x Tevatron luminosity (will probably never happen)

Note: VERY outdated plot. Ignore horizontal scale.

Would probably take until ~2030 to get 3000 fb-1

LEP (at CERN):

- 27 km in circumference- e+e-- Primarily at 2E=MZ (90 GeV)- Pushed to ECM=200GeV- L = 2E31- Highest energy circular e+e- collider that will ever be built.- Tunnel now houses LHC

SLC (at SLAC):

- 2 km long LINAC accelerated electrons AND positrons on opposite phases.- 2E=MZ (90 GeV)- polarized- L = 3E30- Proof of principle for linear collider


- B-Factories collide e+e- at ECM = M((4S)).-Asymmetric beam energy (moving center of mass) allows for time-dependent measurement of B-decays to study CP violation.

KEKB (Belle Experiment):

- Located at KEK (Japan) - 8GeV e- x 3.5 GeV e+- Peak luminosity 1E34

PEP-II (BaBar Experiment)

- Located at SLAC (USA) - 9GeV e- x 3.1 GeV e+

- Peak luminosity 0.6E3439Eric Prebys, "Particle Accelerators", QuarkNet Summer Institute at NIU June 7-17, 2010

- Located at Brookhaven:

- Can collide protons (at 28.1 GeV) and many types of ions up to Gold (at 11 GeV/amu).

- Luminosity: 2E26 for Gold

- Goal: heavy ion physics, quark-gluon plasma, ??


Locate at Jefferson Laboratory, Newport News, VA 6GeV e- at 200 uA continuous current Nuclear physics, precision spectroscopy, etc


A 1 GeV Linac will load 1.5E14 protons into a non-accelerating synchrotron ring.

These are fast extracted onto a Mercury target

This happens at 60 Hz -> 1.4 MW

Neutrons are used for biophysics, materials science, industry, etc…


Put circulating electron beam through an “undulator” to create synchrotron radiation (typically X-ray)

Many applications in biophysics, materials science, industry.

New proposed machines will use very short bunches to create coherent light.


Radioisotope production Medical treatment Electron welding Food sterilization Catalyzed polymerization Even art…


In a “Lichtenberg figure”, a low energy electron linac is used to implant a layer of charge in a sheet of lucite. This charge can remain for weeks until it is discharged by a mechanical disruption.

LEP was the limit of circular e+e- colliders Next step must be linear collider Proposed ILC 30 km long, 250 x 250 GeV e+e-

BUT, we don’t yet know whether that’s high enough energy to be interesting Need to wait for LHC results What if we need more?


Use low energy, high current electron beams to drive high energy accelerating structures

Up to 1.5 x 1.5 TeV, but VERY, VERY hard


Muons are pointlike, like electrons, but because they’re heavier, synchrotron radiation is much less of a problem.

Unfortunately, muons are unstable, so you have to produce them, cool them, and collide them, before they decay.


Many advances have been made in exploiting the huge fields that are produced in plasma oscillations.

Potential for accelerating gradients many orders of magnitude beyond RF cavities. Still a long way to go for a practical accelerator.


Lots has been done. Lots more to do.


eric prebys fnal accelerator physics center june 7-17, 2010

Documents

particle accelerators

quarknet summer institute

kveric prebys

protoneric prebys

buncheric prebys

particle physics experiment

niuthe simplest accelerators

particle arrival time