# Presentation: 914771

## Accelerator Physics Fundamentals

*Eric Prebys*
- FNAL Beams Division

## Outline

- Basic accelerator physics concepts
- Prehistory
- Horizontal motion (lattice functions, emittance)
- Tune plane
- Longitudinal motion (phase stability, longitudinal emittance)
- Luminosity
- Electrons vs. Protons
- The Fermilab accelerator complex
- Examples of other accelerators
- Future or proposed accelerators
- Accelerator physics as a career
- Challenges in the field
- Additional Resources

## Particle Acceleration

- The simplest accelerators accelerate charged particles through a *static *field.  Example: **vacuum tubes**

- 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

## The first cyclotrons

- 1930 (Berkeley)
- Lawrence and Livingston
- K=80KeV

- 1935 - 60” Cyclotron
- Lawrence, et al. (LBL)
- ~19 MeV (D2)
- Prototype for many

## Dipole Field, Thin Lens Approximation. 

- For small deflections:

- 1 T-m = 300 MeV/c

- A uniform magnetic field will bend particles in path of constant curvature:

- side view

- top view

- “kink” at  center of magnet

## Quadrupole Fields (focusing elements)

- Vertical Plane:

- Horizontal Plane:

- Luckily...

- ...pairs give net focusing in *both *planes!

- “FODO cell”

## Betatron Motion

- 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

- (s) is has the fundamental cell periodicity of the lattice

- length of one, e.g., FODO cell

**However, in general the phase (and therefore particle motion) does not, and indeed *****must not*****, follow the periodicity of the ring... **

- Lateral deviation in one plane

- Closely spaced strong quads -> small ** -> small aperture
- Sparsely spaced weak quads -> large ** -> large aperture

- s

- x

## Tune and Tune Plane

- We define the “tune” *Q* (or **) as the number of complete betatron oscillations around the ring.

- For example, the horizontal tune of the Booster is about:

- 6.7

- Magnet Count/Aperture optimization

- Beam Stability

- In general...

- “small” integers

- Many deviations from the ideal lattice are characterized in terms of their resulting “tune-shift”.  In general, the beam will become unstable if it shifts onto a resonance.

## Emittance

- As 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:

- 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)

## Normalized Emittance

- 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:

- Example: Booster

## Slip Factor/Transition

- A particle which deviates from the nominal momentum will travel a different path length given by....

- It will also travel at a slightly different velocity, given by

- “Momentum compaction factor”

- ... so the time it takes to make one revolution will change by an amount

- “slip factor”

- This changes sign at “transition”, defined by

- Usually T  .  In booster T = 5.45

## Longitudinal Motion: Phase Stability

- Nominal Energy

- Particles with lower E arrive *later *and see greater V.

- Nominal Energy

- Particles with lower E arrive *earlier* and see greater V.

- As particles circulate around a ring, they pass through standing RF waves in accelerating cavities.  The stability depends on the relative energy received by off-energy particles

- Below Transition

- Above Transition

## Longitudinal Phase Space

- Stable “bucket”

- Stable particle motion (“bunch”)

- =0 (no acceleration):

- Stable “bucket” (shrinks at high phase)

- Stable particle motion

- =60° (acceleration):

-  Generally, hold RF *amplitude* constant, and adjust *phase* to control acceleration.
-  If amplitude control is needed, it is accomplished by adjusting the *relative phase* of two sets of RF cavities.

## Longitudinal Emittance

- As the particles accelerate

- Longitudinal Emittance.  Usually expressed in eV-s

- Typical values out of the booster are about .15 eV-s

## The Case for Colliding Beams

- One very important parameter of an interaction is the center of mass energy.  For a relativistic beam hitting a fixed target, the center of mass energy is:

- For 1TeV beam on H, ECM=43.3 GeV!!

- On the other hand, for colliding beams (of equal mass and energy):
*Of course, energy isn’t the only important thing....*

## Luminosity

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

- Rate

- Cross-section (“physics”)

- “Luminosity”

- Standard unit for Luminosity is cm-2s-1

- For fixed (thin) target:

- Incident rate

- Target number density

- Target thickness

- For MiniBooNe primary target:

## Colliding Beam Luminosity

- Circulating beams typically “bunched”

- (number of interactions)

- Cross-sectional area of beam

- Total Luminosity:

- Circumference of machine

- Number of bunches

- Record Tevatron Luminosity: 4.2E31 cm-2s-1Record e+e- Luminosity (KEK-B):  1E34 cm-2s-1

## Electrons versus Protons: Synchrotron Radiation

- Whenever you accelerate a charged particle, it radiates.  This is called bremsstrahlung or synchrotron radiation, depending on the context.

- A particle being bent through a radius of curvature  will radiate energy at a rate

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

-  Protons:  Synchrotron radiation does not affect kinematics
-  Electrons: Beyond a few MeV, synchrotron radiation becomes very important      - Good Effects:               - Naturally “cools” beam in all dimensions               - Basis for light sources, FEL’s, etc.      - Bad Effects:               - Beam pipe heating               - Energy loss ultimately limits circular accelerators               - Exacerbates beam-beam effects

## Fermilab Accelerators

- History
-  Early 1960’s – plans solidify for a high energy national accelerator laboratory.
-  1966 – The AEC chooses the Weston, IL site from amongst hundreds proposed.
-  1968 – Construction begins.
-  1972 – First 200 GeV beam in the Main Ring.
-  1983 – First (512 GeV) beam in the  Tevatron (“Energy Doubler”).  Old Main Ring serves as “injector”.
-  1985 – First proton-antiproton collisions observed at CDF (1.6 TeV CoM).
-  1995 – Top quark discovery. End of Run I.
-  1999 – Main Injector complete.
-  2001 – Run II begins.

## The Fermilab Accelerator Complex

- MinBooNE

- NUMI

## Preac(cellerator) and Linac

**“****Preac” - **Coolest looking thing at Fermilab.  Static Cockroft-Walton generator accelerates H- ions from 0 to 750 KeV.  (Actually, there are two of these, H- and I-)

**“****Old linac”-** 200 MHz “Alvarez tubes” accelerate H- ions from 750 keV to 116 MeV

**“****New linac”-** 800 MHz “ cavities” accelerate H- ions from 116 MeV to 400 MeV

- Preac/Linac can deliver about 45 mA of current for about 35 usec at a 15 Hz repetition rate

## Booster

-  400 MeV Linac H- beam is injected into booster over several (up to 15) “turns”.  The ion beam allows one to “cheat” Liouville’s theorem and inject (negative) beam on top of existing (positive) beam.
-  The main magnets of the Booster form a 15 Hz offset resonant circuit , so the Booster field is continuously “ramping”, whether there is beam in the machine or not. Ramped elements limit the average rep rate to somewhat lower.
- From the Booster, beam can be directed to
-  The Main Injector
-  MiniBooNE (switch occurs in the MI-8 transfer line).
-  The Radiation Damage Facility (RDF) – actually, this is the old main ring transfer line.
-  A dump.

-  One full booster “batch” sets a fundamental unit of protons throughout the accelerator complex (max 5E12).
- This is divided amongst 84 53 MHz RF buckets, which sets another fundamental sub-unit (max 6E10).

## Main Injector

-  The Main Injector can accept 8 GeV protons OR antiprotons from
-  Booster
-  The anti-proton accumulator
-  The Recycler (which shares the same tunnel)
-  It can accelerate protons to 120 GeV (in a minimum of 1.4 s) and deliver them to
-  The antiproton production target.
-  (soon) The fixed target area.
-  (soon) The NUMI beamline.
-  It can accelerate protons OR antiprotons to 150 GeV and inject them into the Tevatron.
-  The Main Injector can also accept 150 GeV antiprotons from the Tevatron and *decelerate* them to 8 GeV for transfer to the Recycler.

-  The Main Injector is exactly 7 times the circumference of the Booster.  Allowing one empty “slot” for switching, it can hold six booster batches, in the absence of exotic stacking schemes (slip stacking, RF barrier).
-  It’s envisioned that one batch will be used for stacking and the rest for NUMI and/or switchyard 120.

## Antiproton Source

-  120 GeV protons strike a target, producing many things, including antiprotons.
-  a Lithium lens focuses these particles.
-  a bend magnet selects the negative particles around 8 GeV.  Everything but antiprotons decays away.

-  The antiproton ring consists of 2 parts – the debuncher and the accumulator.

## Antiproton Source – Debunching and Cooling

- Particles enter with a *narrow* time spread and *broad* energy spread.

- High (low) energy pbars take more (less)  to go around...

- ...and the RF is phased so they are decelerated (accelerated),

- Debunching

- resulting in a *narrow* energy spread and *broad* time spread.

- Cooling

- Pickups detect deviations from an ideal orbit, which are used to “kick” the orbit back to the nominal.  This reduces the transverse emittance in a statistical way.

- The anti-proton source can typically “stack” at about 7E10 pbars/h, up to a maximum of about 120E10, at which point anti-protons are transferred to the Tevatron (via the M.I.).

## Tevatron

- The Tevatron was the world’s first superconducting accelerator.
- It accepts protons AND pbars at 150 GeV from the Main Injector. Typically:
- 36 proton bunches with 180E9 protons in each. (Run IIa goal: 270E9)
- 36 pbar bunches with 12E9 pbars in each. (Run IIa goal: 33E9)
- These are accelerated to 980 GeV.
- Collisions (“low beta”) are initiated at the B0 (CDF) and D0 detector regions.
- These “stores” are kept for typically 16 hours, while more antiprotons are made for the next “shot”.

## Recycler

- The Recycler is an 8 GeV storage ring in the same tunnel as the Main Injector.
- The main lattice elements (dipoles and quadrupoles) are made out of permanent magnets).
- The Recycler can accept 8 GeV antiprotons from
- The antiproton accumulator.
- The Main Injector (after deceleration).
- The Recycler can deliver these antiprotons to the Main Injector for acceleration.
- The goal of the recycler is
- To store antiprotons from the accumulator, thereby increasing the total antiproton production capacity.
- To recover antiprotons from a Tevatron store for use in subsequent stores.
- At the moment, the recycler is not being used in standard operation.

## Primary Modes of Operation

**Stacking:** full booster batches (~5E12 p) are accelerated to 120 GeV by the Main Injector, and delivered to the pbar target about once every 3 seconds (limited by the rate at which they can be debunched and cooled.  It takes 10-16 hours to get enough pbars for a “shot”.
**Shot setup:** various beamline tuning takes place.  Most importantly, pbar transfer lines are tuned with *reverse protons**.*
**Proton Injection:**  about 7  53 MHz booster bunches are injected into the M.I., accelerated to 150 GeV and “coalesced” into a single bunch, which is injected into the Tevatron (x 36).
**Antiproton Injection:**  part of the “core” of the accumulator is manipulated to a separate extraction orbit and about 11 53 MHz bunches are extracted to the M.I., where they are accelerated to 150 GeV, coalesced and injected into the tevatron at 150 GeV.
**Acceleration/collision:**  The protons and pbars are accelerated together to 980 GeV over a few minutes. The beam is scraped, and the beta is reduced (“squeezed”) at the collision regions.  Physics begins.  During this time, the rest of the accelerator complex is *totally free to do other things* (primarily stacking).
**MiniBooNE Operation:**  While the M.I. Is ramping, a chain of 8 GeV Booster batches is switched to the MiniBooNE beamline.
**SY120 Operation:**  Batches will be loaded into the Main Injector, accelerated to 120GeV and extracted to the old fixed target area through an old section of the main ring.
**NUMI Operation:**  along with the stacking batch, 5 additional batches are loaded into the Main injector.  These are accelerated along with the stacking batch and extracted to the NUMI line after it has been extracted.

## Some Other Important Accelerators (past):

- 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 will house 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**

## Major Accelerators: B-Factories

- - 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 0.6E34

## Major Accelerators: Relativistic Heavy Ion Collider

- - 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, ??**

## Continuous Electron Beam Accelerator Facility (CEBAF)

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

## Light Sources: Too Many too Count

- 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.

## Future Machines: Spallation Neutron Source (SNS)(Oak Ridge, TN)

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

- These will be fast-extracted to a liquid mercury target.

- This will happen at 60 Hz -> 1.4 MW

- Neutrons will be used for biophysics, materials science, inductry, etc...Turn-on in 2006

## Future Machines: LHC

- - Being built at CERN in the LEP tunnel (27 km circumference)
- 7 TeV p x 7 TeV p.
-  2 Collider experiments (CMS and ATLAS)
-  Turn-on in 2007
-  Design luminosity: 1E34
-  **- Goal: Frontier physics – Higgs, SUSY, ???**

## Future Accelerators (maybe): Next Linear Collider (NLC)/Tesla

-  Two long (10-20 km) linacs colliding e+e-
-  Proof of principle shown at SLC, BUT
-  Low crossing rate means need VERY small bunches (3 nm high!!!!)
-  Challenges:
-  alignment
-  synchrotron radiation issues
-  beam-beam isssues
-  cost management.
- Not formally approved.  Would probably not come online until ~2015 or so.
**Physics Goals: Precision Higgs, electroweak, SUSY searches**

## Things I didn’t talk about

- Medical accelerators
- Unstable isotope accelerators
- Free electron lasers (FEL’s)
- Future and fringe ideas:
- Muon colliders/neutrino factories (a whole talk on its own).
- Wakefield accelerators.
- Molecular accelerators.
- Lots of other stuff.

## Accelerator Physics as a Career: Why Leave Particle Physics??

- In 1983, UA1 always got a big laugh with their author list.
*It had 136 names.*
- MiniBooNE has half that and is now considered “tiny”.
- The CDF and D0 collaborations have ~600 people each.
- The LHC collaborations have ~2000 each already!!!
- Timescales ~10-15 years or more.
- That just *can’t* be fun.

- “I probably wouldn’t go into particle physics today.  There are collaborations with 30 people, sometimes even more.”
- -Louis Alvarez, “Adventures of a physicist”

## Accelerator Physics as a Career: Why not?

- Accelerator physics is not fundamental, in the sense that finding the Higgs or neutrino mass is.
- Accelerator physics is a means to an end, not an end in itself.
- Limited faculty opportunities (that may be changing).

## Why Accelerator Physics can be Fun

- Accelerators are very complex, yet largely *ideal*, physical systems.  Fun to play with.
- Accelerators allow a close interaction with hardware (this is a plus or minus, depending on your taste).
- Can make contributions to a broad range of physics programs, or even industry.
- Many people end up doing a wide variety of things in their careers.
- Still lots of small scale, short time, interesting things to be done.

## Challenges in the Field

- Theoretical challenges:
- Beam stability issues
- Space charge
- Halo formation
- Computational challenges:
- Accurate 3D space charge modeling
- Monitoring and control.
- Instrumentation challenges:
- Correctly characterizing 6D phase space to compare to models.
- Engineering challenges:
- Magnets
- RF
- Cryogenics
- Quality control/systems issues.

## For further reference

- Edwards and Syphers, “An Introduction to the Physics of High Energy Accelerators”:  Standard reference, particularly at Fermilab.
- S.Y. Lee, “Accelerator Physics”.  Slightly more advanced.  Available in paperback.
- US Particle Accelerator School: www.uspas.gov
- Two week courses, twice a year.
- Very good, very intense.
*All the formal training most of us have had.*