Muon Acceleration

V. Lebedev

Jefferson Lab

> MUTAC,
>
> BNL, June 2000

# 

# Contents

1.  Machine layout and main parameters

2.  Linear preaccelerator

3.  First recirculator (RLA1)

    a.  400 MHz versus 200 MHz for the second RLA

4.  Main recirculator (RLA2)

5.  Conclusions

##  

## 1. Machine layout and main parameters

### 

### Basic MAD Parameters

  ----------------------------------------------- -----------------------
  Injection momentum / kinetic energy             190/112 MeV

  Final energy                                    50 GeV

  Initial rms normalized emittance                1500 mm⋅mrad

  Initial rms momentum spread / bunch length      0.11 / 12 cm

  Number of bunches per pulse                     30 ^x^ 4

  Number of particles per bunch / per pulse       10^11^ / 3⋅10^12^

  Bunch frequency / accelerating frequency        200/200 MHz

  Repetition rate                                 15 Hz

  Beam current in micropulse                      0.8 A

  Beam power                                      360 kW
  ----------------------------------------------- -----------------------

### Accelerator layout

![](media/image1.wmf)

### 

### Major Points to be Addressed

1.  Is it possible to accelerate fast enough to prevent a decay of muons

2.  How to capture and accelerate a huge emittance and energy spread

    -   Which energy is appropriate to start recirculation

    -   Number of recirculation stages and number of passes per
        recirculator

    -   Lattice type and chromaticity correction

    -   Accelerating frequency

3.  Coherent beam stability

### Muon Decay

-   Muon decay time - 2.2 μs

-   Accelerating gradient of 15 MV/m

    -   Real estate accelerating gradient in linac -- 8.2 MV/m

    -   Real estate accelerating gradient in recirculators -- 3 MV/m

-   ![](media/image2.wmf)Decay losses depend approximately linearly on
    the accelerating gradient

## Linear Preaccelerator

1.  The final energy (2.8 GeV) is set by RF phase slip for higher passes

2.  Longitudinal (synchrotron) motion in the initial part

    -   suppresses effect of non-linearities in the longitudinal phase
        space

    -   allows to perform the beam bunching

    -   reduces effective accelerating gradient (total voltage of 2.4 GV
        instead 1.9 GV)

![](media/image7.wmf)

![](media/image9.wmf){width="9.0in" height="3.1319444444444446in"}

Beta-function in linear preaccelerator; acceleration from 112 MeV to
2856 MeV

#### 

#### RF

15 MV/m accelerating gradient

16 cryomodules of 5 m length

2 two-cell cavities per cryomodule

45 MV per cryomodule

30 cryomodules of 10 m length

4 two-cell cavities per cryomodule

90 MV per cryomodule

Maximum beam size in the cavity R=20 cm

### Single Particle Tracking for the Linear Preaccelerator

![](media/image10.wmf){width="4.28125in" height="3.5833333333333335in"}
![](media/image11.wmf){width="4.28125in" height="3.5833333333333335in"}

Horizontal and longitudinal phase spaces at the linac end

![](media/image12.wmf){width="8.828472222222222in"
height="2.3777777777777778in"}

Beam losses along the linac

![](media/image13.wmf){width="8.6875in" height="2.4604166666666667in"}

Rms emittance and maximum beam size (maximum particle displacement)
along the linac. Rapid beam size decreases correspond to scraping of the
particles with large amplitude

### Tracking results for the Linear Preaccelerator

1.  Initial particle distribution

    -   Gaussian distribution

        -   Distribution truncated at 2.5 σ in 6D space

            -   30% of particles are cut from the distribution

        -   Transverse rms emittance of 834 mm⋅mrad (1500 mm⋅rad
            normalized) is converted to 540 mm mrad after the truncation

        -   Transverse acceptance of 5200 mm⋅mrad (9400 mm⋅rad
            normalized)

        -   Rms bunch length - 12 cm

        -   Rms energy spread - 0.11

2.  Less than 1% of particles are lost in the course of acceleration

    -   transverse motion "instability" for off-momentum particles with
        large amplitudes

3.  No significant emittance growth

    -   Final rms emittance - *ε~x\ ~*/* ε~y~* = 40 / 39 mm⋅mrad

        -   Horizontal emittance growth -- 9% (Injection chicane)

        -   Vertical emittance growth -- 6%

    -   Final rms energy spread - 0.03

4.  Output acceptance

    -   Transverse acceptance - 430 mm⋅rad

    -   Energy spread - ±0.083

## First Recirculator (RLA1)

### 

### Main parameters for the RLA1

  ------------------------------------------------ ----------------------
  Initial energy                                   2.856 GeV

  Final energy                                     11 GeV

  Number of passes                                 4

  Total initial energy acceptance                  ±6%

  Total final energy acceptance                    ±2 (4.1\*) %

  Initial transverse acceptance                    430 mm⋅rad

  Final transverse acceptance !!!                  160 mm⋅rad ?

  Emittance dilution (5% per arc) !!!              40% ?

  Total voltage per linac                          1.13 (1.23\*)GV

  Circumference                                    \~840 m
  ------------------------------------------------ ----------------------

\*400 MHz scenario

### Longitudinal dynamics in the RLA1 

Effect of the second RLA accelerating frequency on the design of the
first RLA or 400 MHz versus 200 MHz for second RLA

###### Parameters for acceleration in the first recirculator

  ---------- --------- --------- ------------ --------- -------- --------- ------------
             200 MHz\*                        400 MHz\*                    

             Kinetic   Gang      Total energy Kinetic   M~56~    Gang      Total energy
             energy    phase     spread,      energy    \[cm\]   phase     spread,
             \[GeV\]   \[deg\]   2∆p/p \[%\]  \[GeV\]            \[deg\]   2∆p/p \[%\]

  Entrance   2.89      5         11.9         2.89               6         11.7

  Arc 1      4         -26       9.3          4.11      60       -22       9.0

  Arc 2      5         -26       8.7          5.25      60       -25       9.9

  Arc 3      6         -26       7.5          6.36      60       -29       9.8

  Arc 4      7         -26       7.5          7.43      60       -38       9.2

  Arc 5      8         -26       6.9          8.40      50       -45       9.6

  Arc 6      9         -26       6.1          9.26      50       -45       9.9

  Arc 7      10        -26       5.1          10.13     50       -45       9.5

  Exit       11                  4.0          11        50                 8.2
  ---------- --------- --------- ------------ --------- -------- --------- ------------

\* M~56~ = 1.1 m, Total voltage per linac = 1.113 GV at 200 MHz

\*\* Total voltage per linac = 1.227 GV at 200 MHz

![](media/image14.wmf)

Longitudinal phase space in the first recirculator, 200 MHz scenario

![](media/image15.wmf)

Longitudinal phase space in the first recirculator, 400 MHz scenario

### [Optics for RLA1]{.underline}

1.  General requirements for optics

    -   Large energy spread

        -   High symmetry lattice to accommodate large energy spread

    -   Large acceptance

        -   Small beta-functions

    -   M~56~ (\~1 m)

    -   It is a recirculator not a storage ring

        -   Corrected chromaticity of the beam envelopes not tunes

            -   A strategy for optics chromatic correction can be
                different

    -   2T dipoles for highest energy arc

2.  Spreaders and recombiners

    -   Horizontal

    -   Avoid dipoles with strongly separated beams

### ![](media/image16.wmf) 

### Choice of focusing structure

![](media/image17.wmf){width="2.8722222222222222in"
height="2.017361111111111in"}
![](media/image18.wmf){width="2.6993055555555556in"
height="2.057638888888889in"}

![](media/image19.wmf){width="3.997916666666667in"
height="2.060416666666667in"}

Beta-functions for momentum change of +10%

\- Beam envelope oscillates but does not grow

**FODO Triplet focusing**

> ![](media/image20.wmf)

Relative beta-function change for ±10% momentum change
*β*(*p*)/*β*(*p*~0~)

![](media/image21.wmf){width="8.245138888888889in"
height="2.7305555555555556in"}

Beam emittance and beam envelopes with chromaticity correction in the
spreader and recombiner only, particle loss 0.2%

![](media/image22.wmf){width="8.344444444444445in"
height="2.422222222222222in"}

Beam emittance and beam envelopes with global chromaticity correction,
particle loss 0.4%

![](media/image23.wmf)

![](media/image24.wmf){width="9.513194444444444in" height="1.78125in"}

## 

Scheme of sextupole correction (3 families of sextupoles)

**[Layout of magnets in the arcs]{.underline}**

![](media/image25.wmf)

### 

### 

Each next arc is n\*1.5 m longer

⇒Distance between arcs 3\*1.5/π ≈ 1.5 m

⇒Total width for magnets in the tunnel

> 1.5\*4 = 6 m

Cross-section for Arc1 dipole

![](media/image26.wmf)

## Main Recirculator - RLA2

### 

### Main parameters

  ------------------------------------------------ ----------------------
  Initial energy                                   11 GeV

  Final energy                                     50 GeV

  Number of passes                                 5

  Total initial energy acceptance                  ±2.6%

  Total final energy acceptance                    ±0.7%

  Initial transverse acceptance                    160 mm⋅rad

  Final transverse acceptance                      55 mm⋅rad

  Emittance dilution (5% per arc)                  55%

  Total voltage per linac                          4 GV

  Circumference                                    \~3 km
  ------------------------------------------------ ----------------------

# Parameters for acceleration in the RLA2

+-------+------+-----+-----------+--------+----+-------+-----------+
|       | ###  |     |           | #####  |    |       |           |
|       | ## 2 |     |           |  400 M |    |       |           |
|       | 00 M |     |           | Hz\*\* |    |       |           |
|       | Hz\* |     |           |        |    |       |           |
+-------+------+-----+-----------+--------+----+-------+-----------+
|       | Kin  | G   | Total     | K      | M  | Gang  | Total     |
|       | etic | ang | energy    | inetic | ~5 | phase | energy    |
|       | en   | ph  | spread,   | energy | 6~ | \[    | spread,   |
|       | ergy | ase | 2∆p/p     | \      | \[ | deg\] | 2∆p/p     |
|       | \[G  | \   | \[%\]     | [GeV\] | cm |       | \[%\]     |
|       | eV\] | [de |           |        | \] |       |           |
|       |      | g\] |           |        |    |       |           |
+-------+------+-----+-----------+--------+----+-------+-----------+
| Ent   | 1    | -5  | 4.0       | 11.00  | 2  | -7    | 8.2       |
| rance | 1.00 |     |           |        | 00 |       |           |
+-------+------+-----+-----------+--------+----+-------+-----------+
| Arc 1 | 1    | -16 | 4.0       | 15.22  | 2  | -30   | 6.3       |
|       | 4.96 |     |           |        | 00 |       |           |
+-------+------+-----+-----------+--------+----+-------+-----------+
| Arc 2 | 1    | -16 | 3.9       | 18.9   | 2  | -17   | 6.3       |
|       | 8.79 |     |           |        | 00 |       |           |
+-------+------+-----+-----------+--------+----+-------+-----------+
| Arc 3 | 2    | -16 | 3.5       | 22.96  | 2  | -30   | 6.4       |
|       | 2.63 |     |           |        | 00 |       |           |
+-------+------+-----+-----------+--------+----+-------+-----------+
| Arc 4 | 2    | -16 | 2.9       | 26.64  | 2  | -30   | 5.4       |
|       | 6.47 |     |           |        | 00 |       |           |
+-------+------+-----+-----------+--------+----+-------+-----------+
| Arc 5 | 3    | -16 | 2.7       | 30.32  | 2  | -30   | 4.5       |
|       | 0.31 |     |           |        | 00 |       |           |
+-------+------+-----+-----------+--------+----+-------+-----------+
| Arc 6 | 3    | -7  | 2.4       | 34.00  | 2  | -30   | 4.1       |
|       | 4.15 |     |           |        | 00 |       |           |
+-------+------+-----+-----------+--------+----+-------+-----------+
| Arc 7 | 3    | 0   | 1.9       | 37.68  | 2  | -11   | 4.3       |
|       | 8.11 |     |           |        | 60 |       |           |
+-------+------+-----+-----------+--------+----+-------+-----------+
| Arc 8 | 4    | -6  | 1.7       | 41.85  | 2  | -16   | 3.7       |
|       | 2.10 |     |           |        | 60 |       |           |
+-------+------+-----+-----------+--------+----+-------+-----------+
| Arc 9 | 4    | -10 | 1.5       | 45.94  | 2  | -17   | 2.5       |
|       | 6.07 |     |           |        | 60 |       |           |
+-------+------+-----+-----------+--------+----+-------+-----------+
| Exit  | 5    |     | 1.3       | 50.00  |    |       | 1.6       |
|       | 0.00 |     |           |        |    |       |           |
+-------+------+-----+-----------+--------+----+-------+-----------+

\* Total voltage per linac = 3.992 GV at 200 MHz, M~56~ = 2.2 m

\*\*Total voltage per linac = 4.25 GV at 400 MHz

## ![](media/image27.wmf) 

## ![](media/image28.wmf) 

## Important Concerns

### Why SC RF?

-   Large apertures in the linear preaccelerator

-   The only way to get required accelerating gradient (RF generator
    power limit)

-   Smaller voltage droop than for NC RF with the same accelerating
    gradient

-   Positive Jefferson Lab experience verify high reliability of the SC
    RF but

    -   To reach high reliability a by-passing of cavities must be
        anticipated in the design

### Voltage Droop due to Beam Loading

Cannot match RF generators to the beam power because there are no RF
generators with sufficient power

⇒ voltage droop

+----------------------------------+-----------------------------------+
| RLA1                             | RLA2                              |
+----------------------------------+-----------------------------------+
| 200 MHz 4 pass                   | 200 MHz 5 pass                    |
|                                  |                                   |
| ∆V/V = 0.3% per pass             | ∆V/V = 0.3% per pass              |
|                                  |                                   |
| ∆V/V = 1.2% for all 4 passes     | ∆V/V = 1.5% for all 5 passes      |
|                                  |                                   |
|                                  | 400 MHz 5 pass                    |
|                                  |                                   |
|                                  | ∆V/V = 1.2% per pass              |
|                                  |                                   |
|                                  | ∆V/V = 6% for all 5 passes        |
+----------------------------------+-----------------------------------+

-   Synchrotron motion due to non-zero M~56~ prevents a loss of
    acceleration for the last bunch

-   Dependence of beam orbit and optics on the beam current gas to be
    addressed in the design

### 400 or 200 MHz in the second RLA?

+-----------------------------------+-----------------------------------+
| Advantages of 400 MHz             | Disadvantages of 400 MHz          |
+-----------------------------------+-----------------------------------+
| -   Cheaper cavities              | -   Difficult to handle large     |
|                                   |     energy spread in RLA1 at      |
| -   Cheapper RF generators        |     higher passes                 |
|                                   |                                   |
| -   Smaller power consumption     | -   Larger energy droop for 400   |
|                                   |     MHz cavities                  |
|     -   2.5 MW versus 10 MW       |                                   |
|         average RF power for RLA2 |                                   |
|                                   |                                   |
| -   Easier to achieve 15 MV/m     |                                   |
+-----------------------------------+-----------------------------------+

### Possible layouts for recirculator

## ![](media/image29.wmf)

## Conclusion and Required R&D

-   There are no principal physical and technical limitations to build
    an accelerator-recirculator for muons

-   200 MHz accelerating frequency and SC RF look well justified

-   400 MHz in second RLA is desirable but machine optics should be
    built to verify the possibility

-   R&D to get 15 MV/m at 200 MHz

-   Radiation effects on hardware (cavities, dipoles, *etc*.)

-   Beam instrumentation in hard radiation environment