Optimisation of the RAL Muon Front End Design

“Progress” from my last BENE talk (May’04) until now.

Contents

The two new optimisations this summer

Partial progress in phase rotation

But some issues are limiting the optimiser

Beginning to use the MARS code

Nearly ready to break away from 2.2GeV

What to do with 3MW of protons?

You can’t just ignore them (so some ideas)

Some news from Oxford particle physics

Disclaimer

This talk is a collection of unrelated pieces and must in no way be interpreted as a cohesive body of research fit for any particular purpose!

ChicaneLinacB and PhaseRotB

Two new designs began optimisation in May

Decay channel – Chicane – Linac (400MeV)

Decay channel – Phase rotation (180±23MeV)

The second of these allows a cooling ring

PhaseRotB

In this lattice, we had some success

Grahame’s original gets 1.695%

Optimised version gets 2.277% (34% higher)

These are m⁺/p⁺ so 1.64, 2.20 ×10^-3m⁺/p.GeV

This is obtained by varying drift lengths, solenoid fields, radii and lengths, RF phases and voltages, the rod Z position, rod angle and numbers of cells. *

PhaseRotB ‘optimal’ design

Drifts (not very exciting)

All drifts in both sections remained near the minimum length (0.5m), apart from:

Decay channel D2 which is 0.55m, possibly for matching

Phase rotation drifts PD1, PD2 which are 0.834m and 0.618m

PD1 includes last chicane drift

RF cavities are within these “drifts”

PhaseRotB ‘optimal’ design

PhaseRotB ‘optimal’ design

RF cavities

Optimiser increased their number from 30 to 40 (the maximum)

Required to rotate the drifted muons into an energy window of 180±23 MeV

We needn’t expect the optimiser to make them any more ‘regular’ than necessary to get as many as possible into that window

PhaseRotB ‘optimal’ design

PhaseRotB output phase space

Original design:

PhaseRotB output phase space

Grahame’s linearly-designed lattice seems to accelerate the particles slightly too much in the Muon1 simulation

This could be due to the particles arriving at the RF cavities late because of path-length effects

“Spherical aberration”

Note that Muon1 does RF phasing relative to the on-axis particle

PhaseRotB output phase space

New design:

ChicaneLinacB

The optimisation of the chicane design has not yet generated anything better than the baseline (although the baseline was not given as input data)

Barriers to optimisation

With yields so low (~1-2%), there is a lot of noise in the figure of merit

One simulation has ~20k particles to start with, becoming ~60k with multiple decays and emission delays

At 1% this gives 600 out, s=24.3

At 2% this gives 1200 out, s=34.3

Could even be a factor of sqrt(3) larger

Barriers to optimisation

This produces difficulty for an optimiser when occasional +3s results get read

However, the optimisation has definitely been progressing regardless of this

I.e. the ‘improvement’ is not just noise on the same result

This is because noise on the same result would cause successive record scores at geometrically increasing times

Barriers to optimisation

But we see quite regular progress!

Barriers to optimisation

This doesn’t mean that the optimiser hasn’t been hampered by the noise

Perhaps the ‘flattening’ of the curve and subsequent slow convergence are signs

Sources of stochastic noise

Some things are controlled by the RNG:

The 20k pions of the initial rod dataset

Rotations of these pions about the axis

Random delays of this dataset to simulate 1ns RMS incoming proton pulse *

Decays of pions and muons *

* These are weighted, so they each happen 3x in the current simulations. Old simulations had the decay 10x and no delays.

Sources of stochastic noise

Fixing a random seed is not the answer, as this will bias the results!

Increasing the number of particles would be good, but does it counter the decrease in number of designs tested?

Perhaps something cleverer is possible to make the merit function more continuous, discuss…

Nikolai Mokhov’s MARS code

MARS version 15.04 has just been installed at RAL

This is more accurate than the original code (LAHET) used to generate my pion dataset and will scale better to higher energies

It also means I could possibly increase the number of initial pions from 20k to (100?)k

MARS plans

It becomes possible to generate datasets for a variety of energies:

MARS plans

It is also then possible to optimise the proton driver energy jointly with the rest of the lattice, if we are only interested in which option can give the best m/p.GeV

(With all these I should keep in mind how much data I really want Muon1 users downloading from the website…)

MARS problems

The code seems to produce too many p^-, particularly at low energies

This could be my error, or an error in the code itself, or a mislabelling of particle IDs 3 and 4 at some stage, or a real effect

Has anyone else found they have at least twice as many negative as positive pions coming out of their target?!

Intuitively the excess should be of p⁺…

MARS results

Energy deposition histograms are possible and will later become input for Roger Bennett’s target shock studies

Preliminary: 1cm radius tantalum rod, 20cm long, with 6GeV proton beam

The 3MW of used proton beam

Some engineering cross-sections of the target area show where the proton beam can leave and be dumped

However, some of these have solenoids with coils only on the “convenient” side!

The mercury jet target is sometimes drawn with the beam dumped in the mercury pool (but why make it more radioactive than is really necessary?)

The 3MW of used proton beam

One awkward issue is that most optimisation studies have shown a small angle (~0.1rad) is best for pion production

But in my optimisations the optimal angle seems to be near zero!

This could be because the other studies have looked at the pion yield closer to the target and not downstream.

Tilting the rod could give a higher initial yield but with a larger emittance

Solutions with a tilted beam

A gap (unwise!)

Widening or narrowing solenoids (inconvenient)

Rerouting the solenoid coils (weird, but maybe possible)

Solution with an on-axis beam

Conventionally, the trouble with this has been that the protons go down the muon beamline

But the chicane design, for example, has a dipole at the end of the decay channel:

And finally…

Oxford’s particle physics department have been doing studies into first-principles calculation of muon cross-sections in LH2

These include atomic and molecular energy levels, so the model is entirely self-consistent

Results will soon be published and I am hoping to use the ds/dDE table as a reference to benchmark practical tracking techniques against


	The two new optimisations this summer
		Partial progress in phase rotation
		But some issues are limiting the optimiser
	Beginning to use the MARS code
		Nearly ready to break away from 2.2GeV
	What to do with 3MW of protons?
		You can’t just ignore them (so some ideas)
	Some news from Oxford particle physics


	This talk is a collection of unrelated pieces and must in no way be interpreted as a cohesive body of research fit for any particular purpose!


	Two new designs began optimisation in May
		Decay channel – Chicane – Linac (400MeV)
		Decay channel – Phase rotation (180±23MeV)
	The second of these allows a cooling ring


	In this lattice, we had some success
		Grahame’s original gets 1.695%
		Optimised version gets 2.277% (34% higher)
		These are m⁺/p⁺ so 1.64, 2.20 ×10^-3m⁺/p.GeV
	This is obtained by varying drift lengths, solenoid fields, radii and lengths, RF phases and voltages, the rod Z position, rod angle and numbers of cells. *


	Drifts (not very exciting)
		All drifts in both sections remained near the minimum length (0.5m), apart from:
		Decay channel D2 which is 0.55m, possibly for matching
		Phase rotation drifts PD1, PD2 which are 0.834m and 0.618m
		PD1 includes last chicane drift
		RF cavities are within these “drifts”


	RF cavities
		Optimiser increased their number from 30 to 40 (the maximum)
		Required to rotate the drifted muons into an energy window of 180±23 MeV
		We needn’t expect the optimiser to make them any more ‘regular’ than necessary to get as many as possible into that window


	Grahame’s linearly-designed lattice seems to accelerate the particles slightly too much in the Muon1 simulation
	This could be due to the particles arriving at the RF cavities late because of path-length effects
		“Spherical aberration”
		Note that Muon1 does RF phasing relative to the on-axis particle


	The optimisation of the chicane design has not yet generated anything better than the baseline (although the baseline was not given as input data)


	With yields so low (~1-2%), there is a lot of noise in the figure of merit
	One simulation has ~20k particles to start with, becoming ~60k with multiple decays and emission delays
	At 1% this gives 600 out, s=24.3
	At 2% this gives 1200 out, s=34.3
	Could even be a factor of sqrt(3) larger


	This produces difficulty for an optimiser when occasional +3s results get read
	However, the optimisation has definitely been progressing regardless of this
		I.e. the ‘improvement’ is not just noise on the same result
	This is because noise on the same result would cause successive record scores at geometrically increasing times


	This doesn’t mean that the optimiser hasn’t been hampered by the noise
	Perhaps the ‘flattening’ of the curve and subsequent slow convergence are signs


	Some things are controlled by the RNG:
	The 20k pions of the initial rod dataset
	Rotations of these pions about the axis
	Random delays of this dataset to simulate 1ns RMS incoming proton pulse *
	Decays of pions and muons *
		* These are weighted, so they each happen 3x in the current simulations. Old simulations had the decay 10x and no delays.


	Fixing a random seed is not the answer, as this will bias the results!
	Increasing the number of particles would be good, but does it counter the decrease in number of designs tested?
	Perhaps something cleverer is possible to make the merit function more continuous, discuss…


	MARS version 15.04 has just been installed at RAL
	This is more accurate than the original code (LAHET) used to generate my pion dataset and will scale better to higher energies
	It also means I could possibly increase the number of initial pions from 20k to (100?)k


	It becomes possible to generate datasets for a variety of energies:


	It is also then possible to optimise the proton driver energy jointly with the rest of the lattice, if we are only interested in which option can give the best m/p.GeV

	(With all these I should keep in mind how much data I really want Muon1 users downloading from the website…)


	The code seems to produce too many p^-, particularly at low energies
		This could be my error, or an error in the code itself, or a mislabelling of particle IDs 3 and 4 at some stage, or a real effect
	Has anyone else found they have at least twice as many negative as positive pions coming out of their target?!
	Intuitively the excess should be of p⁺…


	Energy deposition histograms are possible and will later become input for Roger Bennett’s target shock studies



	Preliminary: 1cm radius tantalum rod, 20cm long, with 6GeV proton beam


	Some engineering cross-sections of the target area show where the proton beam can leave and be dumped
	However, some of these have solenoids with coils only on the “convenient” side!
	The mercury jet target is sometimes drawn with the beam dumped in the mercury pool (but why make it more radioactive than is really necessary?)


	One awkward issue is that most optimisation studies have shown a small angle (~0.1rad) is best for pion production
	But in my optimisations the optimal angle seems to be near zero!
	This could be because the other studies have looked at the pion yield closer to the target and not downstream.
	Tilting the rod could give a higher initial yield but with a larger emittance


	A gap (unwise!)

	Widening or narrowing solenoids (inconvenient)

	Rerouting the solenoid coils (weird, but maybe possible)


	Conventionally, the trouble with this has been that the protons go down the muon beamline
	But the chicane design, for example, has a dipole at the end of the decay channel:


	Oxford’s particle physics department have been doing studies into first-principles calculation of muon cross-sections in LH2
	These include atomic and molecular energy levels, so the model is entirely self-consistent
	Results will soon be published and I am hoping to use the ds/dDE table as a reference to benchmark practical tracking techniques against