# Presentation: 127735

## Where and How Does MiniBooNE Get its Protons?( It’s a mystery! )Peter Kasper

## The Fermilab Accelerator Components

- Preaccelerator
- H- ions from 0 to 750 keV
- Linac
- H- ions from 0.75 to 400 MeV
- Booster
- Protons from 0.4 to 8 GeV
- Beam to MiniBooNE
- Will not discuss the other accelerators:-
- Main Injector: 8 - 120 GeV ( and Recycler storage ring )
- Tevatron: 0.12 - 0.98 TeV
- Antiproton Source ( and Accumulator storage ring )

## The Fermilab Accelerator Complex

## The Preaccelerator

- Consists of a source housed in an electrically charged dome .. The Cockcroft-Walton
- The source converts H2 gas to H- ions
- 480 V ac current and a series of capacitors and diodes is used to charge the dome to -750 keV
- The ionized gas is accelerated through a column from the charged dome to the grounded wall.

## The Cockcroft-Walton Preaccelerator

- The H2 Bottle

- Diodes

## The Linac: a Series of RF Cavities

- An applied AC current induces an oscillating magnetic field which in turn induces and oscillating electric field
- The cavity acts as an LCR circuit and hence has a well defined resonant frequency
-  Noise is thereby suppressed

## The Linac: 0.75 - 200 MeV

- Outside

- Inside

## The Linac: 200 - 400 MeV

- Low energy Linac RF is 201 Mhz
- High energy Linac RF is 805 MHz
- The gap spacings vary so that the “nominal” particle is inside each successive gap at the same point on the RF phase curve
- Optimal phase region is < E-max
- Fast particles arrive early and see less field
- Slow particles arrive late and see higher field
- Beam becomes bunched

## Buckets and Bunches

- The part of the RF phase curve in which particles will be accelerated is called an RF bucket
- Only particles in synch with the RF buckets will be accelerated
- The particles in an RF bucket is called a bunch

## Magnets: How We Control Beams

- Beams are transported through vacuum beam pipes with the aid of magnet strings which steer the beam and keep it inside the pipe.

- Dipole Magnets
- Uniform field B perpendicular to beam direction Bends beam in an arc of radius R = P/B
-  P is beam momentum
-  B is field strength

- Main Injector Dipole Magnet

## The Need for Focussing

- Accelerators and beam lines with only dipole magnets don’t work
- Perturbations to a beam particle’s direction or momentum from the nominal will cause the particle to eventually be lost
- e.g. any small vertical component to its motion will cause it to drift up (or down) until it hits the beam pipe.
- Booster beam does 4000 circuits = 1.9 km & pipe radius is 5 cm therefore beam would need to be collinear to < 0.025 -radians
- Quadrupole Magnets provide focussing similar to optical lenses

- Beam Pipe

- Focussing

- No Focussing

## Quadrupole Magnets

- Field strength varies linearly with vertical or horizontal displacement from beam center.
- Horizontal focussing implies vertical defocussing
- Magnet pairs of opposite polarity give net focussing

- Linac Quadrupole Magnet

- Coils

## Combined Function Magnets

- The main Booster magnets are combined function
- The resulting fields are a linear combination of a dipole field and a quadrupole field.
- Relative quadrupole/dipole strengths are defined by the angle of the wedge shaped aperture

- Horizontally focussing

- Horizontally defocussing

## The Booster

- Consists of a series of magnets and RF cavities arranged in a circle 75.5 meters in radius
- The magnets keep the beam circulating around the ring while the RF cavities accelerate it.
-  Initial: K.E. = 0.4 GeV, v = 0.713 c
-  Final: K.E. = 8 GeV, v = 0.994 c
-  RF varies from 37.8 to 52.8 MHz as v increases
- A Booster batch:
- Length (time): T = 2 * 75.5 / (0.994 c) = 1.6 s
- # Bunches: T/(52.8*1E6) = 84 = harmonic number

## Inside the Booster Tunnel

- RF cavity

- Magnet

## Getting the Beam into the Booster

- Why does the Linac accelerate H- ions whereas all the other machines accelerate protons?
- Multiple Booster turns worth of Linac beam can be injected simultaneously
-  Higher beam intensities

- Injection magnet has to turn off before beam completes one full turn

- Stripping foil converts H- ions to protons.

- H-

- Foil

- P+

- P+

- P+

- Ring magnets

- Ring magnets

- Injection magnet

- P+

- P+

## The Acceleration Process

- The Booster has 96 main bending magnets each of which bends the beam by 360/96 = 3.75 degrees
- Low power “trim” magnets are used to make corrections to the beam orbit.
- B field increases as P increases
- The main Booster magnets form part of an LCR circuit which resonates at 15 Hz
- Magnet current varies sinusoidally
- Time between booster pulses is 1/15 = 67 msec
-  Linac beam is injected into the Booster at the bottom of the sine wave and extracted 33.3 msec later

## The Acceleration Process II

- The rate of increase in beam momentum has to match the increase in the magnet field strength
- The voltage applied to the RF system varies through the ramp in order to ensure P/B remains constant
- A feedback system is used to do this ( RPOS )
- The horizontal beam position is measured at some convenient point in the ring
- The RF voltage is adjusted such that the beam is held fixed at that point
-  Voltage is increased if the beam drifts inwards
-  Voltage is decreased if the beam drifts outwards

## Betatron Oscillations

- The quadrupole magnets cause beam particles to oscillate about the nominal beam orbit
- The number of oscillations that a particle undergoes in one turn around the machine is called its tune (  )
- The vertical/horizontal tune is the number of vertical/horizontal oscillations
- The natural tunes for a given machine are defined by the arrangement and field strengths of the quadrupole magnets
- They can be ( and need to be ) slightly different
-  Booster: x = 6.7 and y = 6.8

## Instabilities Due to Field Errors

- Integer tunes are unstable w.r.t. dipole field errors

- Small dipole field error in this region

- 1st pass

- 2nd pass

- 3rd pass

- Half integer tunes are unstable w.r.t. quadrupole field errors and so on ..

## Instabilities Due to Field Errors II

- These instabilities are known as tune resonances

- In the general case tune values driven by resonances are given by : m x + n y = k
-  m, n, and k are integers
-  |m| + |n| is the order of the resonance
- Low order resonances are stronger than high order resonances

- 1st, 2nd, and 3rd order resonances are generally fatal
- Since the particles in the beam typically have different momenta they also have different tunes - tune spread
- In order to avoid losses an accelerator needs to operate in a tune region which avoids all low order resonance lines.

## Transition

- Higher momentum particles
-  Get bent less by the dipole magnets
-  Travel in larger radius orbits
-  Have higher velocities
- The path length differences remain constant as the beam momentum increases
- The velocity differences decrease as the particles become more relativistic
- Transition is the energy at which these two effects cancel
- Below transition high momentum particles reach the RF cavities 1st
- Above transition low momentum particles reach the RF cavities 1st

## Transition II

- The RF phase has to be changed in order to maintain the beam in stable RF buckets
- The transition energy represents a point of instability in the acceleration cycle and is determined by the size of the ring and the strength of the magnets
-  For the Booster K.E.transition = 3.26 GeV

- RF voltage

- Time

- Region of stability before transition

- Region of stability after transition

## Other Sources of Instabilities

- Wake Fields
- Bunched beam represents an AC current
- Induces delayed image fields on the walls of the beam pipe
- Induced wake field can interact coherently with trailing bunches or trailing particles of the same bunch to produce coherent motion
- Results in all kinds of bizarre resonances
- Space Charge
- Electrostatic forces tend to blow the beam apart
- Creates large momentum spread  large tune spread  losses
- Effect is reduced at high energy due to lorentz contraction of E-fields

## Conclusion

- It’s a miracle that machines work at all!