# Presentation: 302099

## Main Injector Beam Dynamics

**Jean-François Ostiguy**
**Accelerator Division **

## Credits

**James MacLachlan** :Injection schemes studies and    transition crossing simulations
**Gerald Jackson** : Injection energy jitter & control
**King-Yuen Ng**:  Instability thresholds calculations
**Nikolai Mokhov**: Collimation System

- This presentation is based upon and borrows liberally from
- the work of several people:

## Uncontrolled Loss Budget

**Working assumption: “acceptable uncontrolled averaged” power loss ****(assuming particle energies above threshold for activation): ****1 W/m**
**FMI 3319.4 m **** ****Max allowable loss : 3.3 kW**** **
**Total beam power at injection energy   ****W = 8  GeV x 1.5 E14 particles /1 .5 s**
**            ****= ****133 kW**** **
**At transition (****γ****t**** ****= 21.8)   ****W= ****320 kW**** **
**At top energy  W = ****2 MW**

|  | Budget | Max |
| --- | --- | --- |
| Injection
(8 GeV) | 1.0 %
1.3 kW  | 2.4 %
3.3 kW |
| Transition | 0.3%
1 kW | 1.0%
3.3 kW |
| Top Energy
(120 GeV) | 0.05%
1 kW | 0.17%
3.3 kW |

## 2-Stage Collimation Concept

- One primary and 2 secondary collimators for each plane.
**Assumptions: 1% collimated at injection 0.5% at top energy**

- Total power intercepted ~ 11 kW
- Require steel shielding 1m x
- 2.5 m which covers the secondary
- collimators and the 1st quad
- downstream.
- Sec Collimator: Stainless Steel,
-                           ~0.5 m long

- Size, cost and high power level favors  a localized collimation system.

## Injection

**Adiabatic capture from coasting beam ****(baseline)**
**Synchronous injection into waiting buckets**

- Two scenarios have been explored:

- Initial results indicate that losses can be made negligible
- for either scenario. Which scenario is optimal depends on many factors, such as the effective energy spread of the injected beam and the availability of a high frequency beam chopper.

## Adiabatic Capture

**If the energy spread is too low, stability may be impaired **
**Injected beam needs to be chopped at revolution frequency( ~90 kHz) (E-deflection possible)   **
**barrier RF needed to preserve abort gap during injection; ****barrier voltage depends on dp/p**
**Capture time:  ~30 ms **
**A weak modulation (53 Mhz) of the beam is necessary to get detectable  BPM signal  during injection**

## Synchronous Transfer

**Require 6 ns gaps every 19 ns.  This implies availability of a high frequency chopper**
**As for adiabatic capture, beam must also be chopped at 90 kHz to provide abort kicker gap. **
**No barrier cavity required to preserve abort gap**
**Momentum painting allows matching into bucket at higher voltage for better stability**
**2****nd**** Harmonic cavity (~50% of fundamental) valuable****(though not necessary) to match rectangular painted space into elliptical contours**
**Matching operation also requires ~30 ms  (not needed without 2****nd**** harmonic)**

## ESME Simulations: Synchronous Injection

## ESME Simulation: Abort Gap Preservation (adiabatic capture)

## Transition Crossing Loss Simulations at Intensity x 5

| ε(100%) | γt-jump | L insert | Final ε (rms) | Loss (%) |
| --- | --- | --- | --- | --- |
| 0.30 | N | Y | 0.084 | 0.09 |
|  | Y | Y | 0.066 | 0.00 |
| 0.35 | N | N | 0.101 | 0.74 |
|  | N | Y | 0.095 | 0.40 |
|  | Y | N | 0.077 | 0.00 |
|  | Y | Y | 0.078 | 0.00 |
| 0.38 | N | N | 0.104 | 1.39 |
|  | N | Y | 0.102 | 0.87 |
|  | Y | N | 0.084 | 0.00 |
| 0.40 | N | N | 0.107 | 1.94 |
|  | N | Y | 0.106 | 1.31 |
|  | Y | Y | 0.089 | 0.00 |

## γt Jump system

**Δ γ**** = +/- 1 within 0.5 ms;  d****γ****/dt = 4000/s (about 17  faster than the normal ramp rate)**
**8 pulsed quadrupole triplets**
**localized, independent dispersion perturbation**

**A ****γ****t****  jump conceptual design was completed in 1997 ****(PAC 1997 pp 994-996)**

## Energy Spread and Longitudinal Acceptance

**The longitudinal acceptance sets an upper limit on the allowable (effective) energy spread in the injected linac pulse.**
**The measured  longitudinal acceptance of the FMI is 0.7 eV-s at current intensity (1 E11 ppb).**
**Simulations show that with a gamma-t jump system, it should be possible to accelerate at least 0.5 eV-s without loss through transition**
**Assuming adiabatic capture, 0.5 eV-s corresponds to an energy height of +/- 13.5 MeV (0.7eV-s corresponds to +/-19 MeV)**
**The momentum collimation system will limit the spread to +/- 10 MeV**

## MI Beam Stability at Intensity x 5

**NM Instability (above transition):**
- At 5 times the intensity, the situation is
- roughly the same as now, if the crossing rate is
- increased by a factor of 15.8

**Single bunch Mw Instability**:
- longitudinal & transverse below threshold
**Coupled bunch Instabilities**: transverse above threshold (currently as well), predicted growth time: 110 turns (5x faster). Current digital damper system can be upgraded to suppress both transverse and longitudinal instabilities.
**Beam loading**:
- With new cavities, R/Q = 25 ohms ( current is 104 ohms) so situation is roughly similar to current one.

- Tune shifts:
- vertical tune expected to pass through 3rd order stop-band. Working point will need to be optimized.

## Conclusions

**No fundamental obstacle to operating the MI at 5 times the current intensity has been uncovered. This being said, a lot of work remains to be done.  **
** ****More detailed simulations will be required to   maximize effective acceptance (transition losses below a few tenths of 1%) and determine whether an inductive insert is necessary. **
**Optimization of the injection scenarios will continue; while adiabatic capture remains the baseline design, full understanding of the tradeoff with synchronous capture require additional studies**
**Full scale space-charge 3D simulations will start soon.        **