# Presentation: 587269

## A Cartoon Description of Linear Accelerators

- Rob Kutschke
- NML Controls Meeting
- February 19, 2007

- ILC-doc-392-v4

## Caveat

- My background is detectors not accelerators.
- Many of you may know more than I do about some part or other.  Please feel free to add comments and to correct any mistakes I have made.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## A Few Numbers

- Operating frequency: = 1.3 GHz
- Wavelength:  =c/ = 23.1 cm
- Feature sizes are typically rational fractions of the wavelength:  
- For electrons:
- E=100 MeV, 1-v/c=12.E-6
- Difference of 12 microns over 1 m.
- Bunch length is 300 microns.
- So to a good approximation the electron speed is constant over long lengths of the linac.
- Notable exception in first few meters.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## RF Cavity Cutaway on 15th Floor

- The RF Cavities are the heart of the ILC

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Detail of the 15th Floor Cavity

- Detail of the 15th Floor Cavity

- 

- Port

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## RF energy enters via ports
ILC has only one port per 9 cell cavity (?).
Energy bounces around inside the cavity cells. Bouncing waves interfere with each other.
Shape designed to get standing wave interference pattern with the property that the on axis electric field is:
Parallel to the axis.
Oscillates in strength (+ and - ).
I forget what the field is off from axis.
Close to axis the transverse components are small.
Q = quality factor of resonantor.
Q of unloaded ILC cavity needs to be 1010.  High Q implies:
Higher on-axis field for a given input power at correct frequency.
Tighter demands on accuracy and stability of the input frequency.
Tight mechanical and material tolerances. 
Cavities can be tuned to respond to the correct frequency (within small tolerances).

- ILC has only one port per 9 cell cavity (?).
- Energy bounces around inside the cavity cells. Bouncing waves interfere with each other.
- Shape designed to get standing wave interference pattern with the property that the on axis electric field is:
- Parallel to the axis.
- Oscillates in strength (+ and - ).
- I forget what the field is off from axis.
- Close to axis the transverse components are small.
- Q = quality factor of resonantor.
- Q of unloaded ILC cavity needs to be 1010.  High Q implies:
- Higher on-axis field for a given input power at correct frequency.
- Tighter demands on accuracy and stability of the input frequency.
- Tight mechanical and material tolerances.
- Cavities can be tuned to respond to the correct frequency (within small tolerances).

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Basic Idea for Acceleration

- t=0

- Electric Field

- Cavity

- Positron Bunch

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Positrons accelerate in the direction of the electric field.
Electrons accelerate in the direction opposite to the electric field.
Node in the standing wave between cells.
Detailed shape of cavity and choice of the RF frequency ensures that the electric field has the correct phase (timing) with respect to the arrival of each bunch. 
Electrons/positrons extract energy from the standing wave.

- Electrons accelerate in the direction opposite to the electric field.
- Node in the standing wave between cells.
- Detailed shape of cavity and choice of the RF frequency ensures that the electric field has the correct phase (timing) with respect to the arrival of each bunch.
- Electrons/positrons extract energy from the standing wave.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Snapshot of Electric Field Strength

-  “Phase Focusing” keeps bunches bunched.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Operate close to max field strength:
Gives maximum acceleration
But not too close:
No phase focusing exactly at max.
Actually defocuses if bunch straddles max.
High frequency, short bunch length and long accelerator length make it harder to precisely control the timing of the RF relative to the arrival of the bunch at every cell.
Q increases with falling temperature
Cost optimum around 2K.
Bunch extracts energy from the standing wave.

- Gives maximum acceleration
- But not too close:
- No phase focusing exactly at max.
- Actually defocuses if bunch straddles max.
- High frequency, short bunch length and long accelerator length make it harder to precisely control the timing of the RF relative to the arrival of the bunch at every cell.
- Q increases with falling temperature
- Cost optimum around 2K.
- Bunch extracts energy from the standing wave.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## ILC 9 cell cavity in its vertical orientation.
Only one input port per 9-cell cavity.
2 other ports discussed later.

- ILC 9 cell cavity in its vertical orientation.
- Only one input port per 9-cell cavity.
- 2 other ports discussed later.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Why 9 Cells per Cavity?

- If too few cells/cavity the packing fraction is too small.
- Need things like bellows between cavities to allow for thermal expansion.
- Other reasons?
- If too many cells/cavity:
- Production yield issues.
- Peak accelerating field drops with number of cells ( really another sort of yield issue ).
- Other reasons?  Approximation of constant speed fails????

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## What Are the Other Parts For?

- Delivering power to RF cavities.
- Corrections for imperfections.
- Includes focusing of off-axis particles.
- Feedback and monitoring.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Klystron

- A narrow band RF amplifier.
- Phase of output waveform controlled by a reference wave ( from low level RF ).
- Amplitude of output frequency governed by power delivered by the RF Modulator ( think of it as a power supply for the klystron ).
- More info:
- _[http://](http://en.wikipedia.org/wiki/Klystron)__[en.wikipedia.org/wiki/Klystron](http://en.wikipedia.org/wiki/Klystron)_
- _[http://www2.slac.stanford.edu/vvc/accelerator.html](http://www2.slac.stanford.edu/vvc/accelerator.html)_

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Klystron in the linac gallery ( well, the housing of a klystron ...) 

- Klystron in the linac gallery ( well, the housing of a klystron ...)

- Waveguide

- Like a very low loss cable for RF energy.
- Evacuated rectangular structures.
- Transverse dimensions fractions of a wavelength of RF ( 1⁄2, 1⁄4 I forget which ).

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Amount of power from klystron that gets into the cavity is called the transmitted power or forward power.
What happens if you put power into a cavity but no bunch comes through?
Energy bounces around the cavity and comes back out the wave guide.
Reflected power.
Time scale for discharge is a few ms ( O(Q periods) ).
Loaded cavity has a Q of O(3 x 106 ).
Need to protect klystron from reflected power
Circulator directs reflected energy to a load.
Bunch does not remove 100% of the energy so some always bounces back. (Check this?).
Modulator should be programmed to supply less energy if a small bunch is expected. 
Or else input energy is just transported to dump.  Wasteful. 
Is this controlled by low level RF?
If klystron frequency does not match cavity’s, almost all power is reflected and only a little is stored in the cavity.

- What happens if you put power into a cavity but no bunch comes through?
- Energy bounces around the cavity and comes back out the wave guide.
- Reflected power.
- Time scale for discharge is a few ms ( O(Q periods) ).
- Loaded cavity has a Q of O(3 x 106 ).
- Need to protect klystron from reflected power
- Circulator directs reflected energy to a load.
- Bunch does not remove 100% of the energy so some always bounces back. (Check this?).
- Modulator should be programmed to supply less energy if a small bunch is expected.
- Or else input energy is just transported to dump.  Wasteful.
- Is this controlled by low level RF?
- If klystron frequency does not match cavity’s, almost all power is reflected and only a little is stored in the cavity.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## What happens if you send an on axis beam down an unpowered cavity?
It creates a standing wave in the cavity ( which runs out the waveguide if one attached ).
What about an off axis beam?
Creates higher order modes (HOM) in the cavity.
Excites other patterns of standing waves at different frequencies.
Need to get rid of this energy by putting a second port on the cavity (at a location that does not disturb  the primary standing wave much ). 
Connect a waveguide to the HOM port and send the higher order mode energy to a load.
Drum head example?
Offaxis beam in powered cavity is the same.

- It creates a standing wave in the cavity ( which runs out the waveguide if one attached ).
- What about an off axis beam?
- Creates higher order modes (HOM) in the cavity.
- Excites other patterns of standing waves at different frequencies.
- Need to get rid of this energy by putting a second port on the cavity (at a location that does not disturb  the primary standing wave much ).
- Connect a waveguide to the HOM port and send the higher order mode energy to a load.
- Drum head example?
- Offaxis beam in powered cavity is the same.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Could use the  HOM port for diagnostics?
ILC design has three ports: 
Main power input port
2 HOM ports.
Can also check cavity performance with and without beam by measuring the reflected power.
For the first few meters of the linac the electron speed is much less than c and special treatment is needed.

- ILC design has three ports:
- Main power input port
- 2 HOM ports.
- Can also check cavity performance with and without beam by measuring the reflected power.
- For the first few meters of the linac the electron speed is much less than c and special treatment is needed.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Dewars, Cryostats, Cryomodules

- Dewar:
- Vessel with vacuum insulation (thermos bottle).
- Contents is not under vacuum; vacuum is in the walls.
- Cryostat:
- A device used to maintain constant low temperature.
- Usually two layers of dewars: liquid nitrogen layer outside and liquid helium layer inside.
- I guess ILC ones are like this (don’t really know).
- Cryomodule:
- 3 cavities ( 9+9+8) cells enclosed in a single cryostat.
- 8 cell cavity also holds some magnets
- Focusing, correcting??? Not sure.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## RF Unit

- In ILC design 3 cryomodules are powered by a single klystron ( plus its modulator  and associated low level RF ).
- Powered distributed via waveguides.
- Transition from waveguide to cavity is made by an RF power coupler.
- Has controls to adjust phase of RF to ensure that all cavities have correct relative phase.
- Why 3 cryomodules per RF Unit?
- Power limit of spec’d klystrons.
- Commercial klystrons do not (yet) reach the specs for lifetime.   One of the R&D projects.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Slide 21

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Multipole expansion

- One can write an arbitrary magnetic field as a power series expansion with powers of 1/2n.
- Dipole – two lobes in field pattern.
- Quadrupole – 4 lobes in field pattern.
- Octopole – 8 lobes
- Hexdecapole – 16 lobes
- ...
- Why no n=0 term or other odd terms?
- Magnetic monopoles (magnetic analog of electric charges ) have not been observed, even though we have looked very hard.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Dipole Magnet – Old Style

- Current carrying circular coils go into the orange housings.
- Current runs in same sense in upper and lower coil packages.
- This magnetizes the iron.
- Magnetic field is constant and vertical between the pole pieces.
- Trajectory for a horizontal particle is (arc of) a circle.
- For TeV dipoles, distort pole shape to a racetrack.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Mockup of a TeV Dipole

- Coils:  “racetrack” shape.

- Beam Pipe

- On axis field is constant and vertical.
- Edge effects – see later.
- Without iron pole tip, field is still constant and vertical but changes more rapidly off axis.
- Iron is useful up to about 1 T  (check value).

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Dipole Magnets

- When iron is present:
- The shape of the field between the pole tips is governed by the shape of the iron.
- Can be sloppier about coil construction.
- For fields over about 1 Tesla, iron saturates.
- To get stronger fields, just use coils without iron.
- Tougher construction tolerances for coils.
- To get really strong fields you need very high currents: use superconducting coils to keep losses low.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Quadrupole Magnets

- What happens if a particle is not traveling exactly along the cavity axis, or if the axes of all cavities are not perfectly lined up.
- Particle starts to drift transversely.
- Focused back to the beam axis by quads.
- Four current loops.
- Quads focus (FO) in x and defocus (DO) in y ( or vise versa ).
- Or pick any pair of orthogonal transverse coords.
- If a FODO pair have the correct separation there is net focusing in both planes.
- During acceleration, the beam is only focused enough to keep it in the “sweet spot” of the machine.
- At IP the beam is tightly focused.
- (Spot size times divergence) is conserved.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Corrector Magnets.

- Dipoles and quads have end effects, construction tolerances, materials defects ...
- These produce higher order multi-pole components.
- Need to have higher order magnets to correct for the errors induced by these effects:
- Sextupole
- Octopole
- Hexadecapole
- ...
- Positions of these magnets are fixed.  To make the corrections, one varies the currents in them.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Kicker Magnet

- Magnet used to move particles from one trajectory to another.  Example: injection or extraction into MI, TeV, Booster ...
- All the ones I know of are dipoles.
- Magnet and associated power supply must have fast rise and fall times.
- Do not want to disrupt leading and trailing bunches, just the one you want.
- For ILC some very fast kickers are needed.
- Often the bore needs to be wider than a typical magnet to accommodate the two trajectories.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Magnet Summary

- Dipole: bends beam
- Quad: focuses beam in one plane.
- FODO pair of quads: focuses beam in both planes.
- Higher order poles:
- Correct for end effects, manufacturing tolerances ....

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Spot Sizes at IP

- Along linac focusing is just enough to keep beams in the linac.
- Spot size is relatively large.
- Just before IP the beams pass through very strong quads to tightly focus the beam and make a small spot size at the IP.
- Spot size is much, much smaller than anything previously achieved.
- See figures on next two pages.
- SLC refers to the Stanford Linear Collider, a previous “linear” collider than ran in the 1990’s.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Slide 31

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Slide 32

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Making Positrons

- The ILC will accelerate bunch trains of about 1 ms in length, 5 times a second.
- Duty cycle is about 1/200.
- During the off-cycle, electrons will be accelerated partway down the main linac and diverted to an undulator.
- Static, period magnetic structure with very high magnetic field gradients.
- This wiggles the beam to radiate forward going photons.
- Then you steer the electrons out of the way.
- Put a sheet of high-Z material (Pb?) in the path of the photons: produces electron-positron pairs ( plus junk).
- Keep the positrons and throw the rest away.
- Do this with magnetic and electric fields.
- Then focus and cool the positrons.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## RF Gun

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## NML Test Accelerator Schematic

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Still to come

- Faraday Cup
- Metal, cup-shaped electrode.
- Used to measure ion currents.  Think of a closed electric circuit in which part of the path is not a wire but a stream of ions or electrons traveling in vacuum. The rest of the path is a more traditional electric circuit.
- Not sure how it is used here.  I guess it is used to measure the electron current somewhere in the RF gun.
- Dark Current.
- Magnetic Chicane bunch compressor.
- Superconducting.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## The 3.9 GHz Cavities

- 3.9 GHz.  The NML test accelerator contains some 3.9 GHz cavities that are used to bunch the beam more tightly.
- Being developed as part of A0 project.
- We will make one set for us and another set to send to DESY who will use it in the same way at TTF.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## Not Ready for Prime Time

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## IQ Plot

- Could mean a few things.  This is my guess.
- Many observable things can be represented as a complex number.
- An RF signal at a fixed frequency has a magnitude and phase.
- I and Q are just the real and imaginary parts of the complex number.  ( Sometimes the polar representation might be more useful).
- Language comes from the idea that you are measuring the amounts of some signal that are “In phase” and “in Quadrature” with a reference signal.
- Or it could refer to something totally different.
- I need to know the context in which you saw this to be sure.

- Rob Kutschke, Linac Cartoons

- 2/19/2007

## More Trivia

- When a pulse of energy comes down wave guide from klystron, it induces currents in the walls of the cavity.
- These currents repel and attract each other ( known as Lorentz forces ).
- These forces distort the cavity and change its resonant frequencies (tune).
- Piezoelectric actuators are present to pre-distort the cavity in the opposite direction so that the Lorentz force distorts the cavity back to the correct shape.

- Rob Kutschke, Linac Cartoons

- 2/19/2007