# Presentation: 388223

## Optimization of phase rotation parameters for the -factory

*Optimization of phase rotation parameters for the ********-factory*

- M. Apollonio – University of Oxford

- ISS meeting - Princeton - (27/7/2006)

## Leading idea: 

***Leading idea: ***
***5 figures used to parametrize the ************-rotation ***
***Goal:***
***Trying to reach the “best” combination of these values to produce an “ideal” muon beam***
***Instead of doing it by hand (lengthy/tedious) use a minimization procedure ************ MINUIT***
***Wrap ICOOL+endof9+ecalc9 in a MINUIT main routine***
***Discuss results ...***

- ISS meeting - Princeton - (27/7/2006)

## Parameters       initial (“typical”) values                    meaning/function

***Parameters       ******initial (“typical”) values                    meaning/function***
***ref1 ----------------------  -.48         ******reduce energy (negative ramp)***
***ref2 ----------------------  2.64          ******increase energy (pos. ramp)***
***delta ---------------------  18.04    ******# of w.l. separating the ref. particles***
***grad ----------------------  12                     ******RF gradient****** ***
***ref1(2)=ref2(2) --------  .214   ******    energy level in the cool. section***

***ref part 1***

***ref part 2***

********* ******-rotation***

***final energy level***

*t or Z*

*E*

- ISS meeting - Princeton - (27/7/2006)

## Which minimization?

***Which minimization?***
***Probably a matter of taste, but I ended up with a SIMPLEX minimization which looks faster than usual MINImize  and reliable***
***Structure of the program***

*minuit routine:*
*change parameters*
*modify ICOOL for001.dat file (new input)*
*run ICOOL+ENDOF9+ECALC9*
*compute sigma(E) at the END of the*
*     **COOLING channel*

*END*

*verify minimization convergence*

- ISS meeting - Princeton - (27/7/2006)

## Technical note:

***Technical note:***
***To speed the algorithm up I used a smart set of  40 muons (only) provided by Bob ***
***Energy distribution***
***       ******at the beginning of ***
***       ******the channel ***

- (MeV)

***Muons are injected at the beginning of the drift channel ***

- ISS meeting - Princeton - (27/7/2006)

## Function to minimize:

***Function to minimize:***
***Sigma(E)/3 MeV ******(at z=216,  226,  232,  239.6,  247 m)***
***1******st****** attempt: leave 1 or 2 running while fixing the other par’s***
***Check shape of minimized function***
***Subsequently release 1-4 par’s (p5 fixed) and run minimization***
***Results***

********* ******-rotation***

***final energy***

*Z*

*E*

***E**(initial)*

***E**(final)*

- ISS meeting - Princeton - (27/7/2006)

## Fix all but P2=REF2

***REF2***

**2.85**

**2.59**

**3.20**

**2.45**

***initial values***

**-0.4**

**-0.5**

***initial values***

***Fix all but P2=REF2***

***Fix all but P1=REFP***

***NB: MINImize routine used here***

**~2.67**

**~-0.446**

- ISS meeting - Princeton - (27/7/2006)

## Fix 3,4,5 and minimize over P2 scanning on P1

***FCN vs P1***

***P2 vs P1***

***Fix 3,4,5 and minimize over P2 scanning on P1***

- ISS meeting - Princeton - (27/7/2006)

## Comment: when fixing all the parameters but one

***Comment: when fixing all the parameters but one***
***minimization produces a new value which is very***
***close to the starting one***
***i.e.: the initial choice of parameters is sensible***
***BUT parameters can be correlated ... ***
***Also, P5 is related to energy in the cooling section: for the moment cooling is ignored therefore P5 is set (and fixed) to its original value .214. Focus only on the energy spread reduction after ************-rotation***

*drift       ****-rotation       cooling*

- ISS meeting - Princeton - (27/7/2006)

## drift

*drift*

**Evolution of the set of 40**
**muons with *****NON***
**optimized parameters**
**N.B. there’s a shift in the **
**average value of the **
**energy (~30 MeV) [?]**

***-rotation*

- ISS meeting - Princeton - (27/7/2006)

## P5=fixed and minimzation run over P1, P2, P3 and P4

***P5=fixed and minimzation run over P1, P2, P3 and P4***
***   ***
***      ******ini.             final ***
***P1  -0.567        -0.43***
***P2  2.57           3.11***
***P3  18.01        18.11 ***
***P4  8.93          6.327***
***P5  0.214        0.214***
*** ***

*drift*

***-rotation*

- ISS meeting - Princeton - (27/7/2006)

## Slide 12

- ISS meeting - Princeton - (27/7/2006)

## Evolution of the ensemble of muons through the channel regions

***Evolution of the ensemble of muons through the channel regions***

***non optimized parameters                               optimized parameters ***
*** ******-0.567, 2.57, 18.016, 8.93, ***_***0.214***_***                       -0.43, 3.11, 18.116, 6.33, ***_***0.214***_

***t (************sec)***

***t (************sec)***

***E (MeV)***

***E (MeV)***

- ISS meeting - Princeton - (27/7/2006)

## Now turn the COOLING ON ...

***Now turn the COOLING ON ...***

***non optimized parameters                               optimized parameters ***
***-0.567, 2.57, 18.016, 8.93, ***_***0.214***_***                        -0.57, 2.57, 18.06, 9.88, ***_***0.214***_

***E (MeV)***

***t (************sec)***

***E (MeV)***

***t (************sec)***

*drift       ****-rotation       cooling*

- ISS meeting - Princeton - (27/7/2006)

## Conclusions:

***Conclusions:***

***ICOOL+endof9+ecalc9 wrapped in MINUIT:***
***Optimization of parameters for ************-rotation ***
***PAR5 fixed, PAR1-4 optimized requiring sigmaE to be minimized***
***At first optimization is done ignoring the cooling (interesting/promising) ***
***Then cooling is switched on (to be understood) ***
***Pretty fast: couple of hours with 4 param’s***
***Ultimately we want to understand how many muons are left after the cooling stage, and  -possibly- to optimize this number  ***

- ISS meeting - Princeton - (27/7/2006)

## To be done:

***To be done:***

***Verify the new parameters on a full and more realistic simulation***
***Think about a better function to minimize (taking into account also the number of muons) ***

- ISS meeting - Princeton - (27/7/2006)