COMPUTER SIMULATION OF THE VARIATION OF POLARISATION WITH EMITTANCE WHEN CROSSING TWO SUCCESSIVE INTRINSIC RESONANCES

(1)

HAL Id: jpa-00224601

https://hal.archives-ouvertes.fr/jpa-00224601

Submitted on 1 Jan 1985

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

COMPUTER SIMULATION OF THE VARIATION OF POLARISATION WITH EMITTANCE WHEN

CROSSING TWO SUCCESSIVE INTRINSIC RESONANCES

A. Nakach

To cite this version:

A. Nakach. COMPUTER SIMULATION OF THE VARIATION OF POLARISATION WITH EMIT-

TANCE WHEN CROSSING TWO SUCCESSIVE INTRINSIC RESONANCES. Journal de Physique

Colloques, 1985, 46 (C2), pp.C2-657-C2-662. �10.1051/jphyscol:1985282�. �jpa-00224601�

(2)

JOURNAL DE PHYSIQUE

Colloque C2, supplément au n°2, Tome 46, février 1985 page C2-657

COMPUTER SIMULATION OF THE VARIATION OF POLARISATION WITH EMITTANCE WHEN CROSSING TWO SUCCESSIVE INTRINSIC RESONANCES

A. Nakach

Laboratoire National Sattwne, CEN-Saclay, France

RESUME

Pour i n t e r p r ê t e r les r é s u l t a t s expérimentaux, précédemment d é c r i t s , une s i m u l a t i o n a été f a i t e sur c a l c u l a t e u r .

Plusieurs distributions des amplitudes d ' o s c i l l a t i o n à l ' i n t é r i e u r du faisceau ont été essayées. Une d i s t r i b u t i o n plus riche au centre reproduit assez bien l e s r é s u l t a t s trouvés.

ABSTRACT

Computer simulations have been done to understand experimental results concerning the increases of polarisation after crossing two successive intrinsic resonances (VG =

vz

and FG = 8 - »

z

) .

Several distributions have been tried and a good agreement has been achieved with experimental curves.

INTRODUCTION

We recall fig. n° 1 experimental results concerning the variation of polarisation with the number of accelerated protons (ref. 1 ) , when we decrease vertical emittance by a closed orbit deformation which controls the loss of particles on a scraper.

Only those with the largest betatron amplitudes are lost.

These results can be understood if we admit existence of a core inside the beam, the polarisation of which is conserved through any resonances crossing of intrinsic type (at Saturne II VQ, = " at 915 MeV and FG = 8 -

c

at 1385 MeV) and peripheral particles with an adiabatic reversal of their spin, two times successively, restoring--- initial pola- risation (that of the core).

A computer simulation has bee^i done with several amplitudes distri- butions D (z) of the beam, its total size Z „ known and almost fixed.

' max Two extreme kinds of distributions have been tried. The uniform one

D i & = ^ a x a n d ™ e V*> = 1+4 1 ? r ^

x

\

—K

max

max k is a normalisation coefficient such that

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985282

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JOURNAL DE PHYSIQUE

We call :

A

Q = jZ D (:) dz

0 A

For one particle of amplitude Zmm the polarisation, following the Froissart and Stora formula (ref. 2 and 3) is given by, for Saturne I 1 ring

2 Zmm after Y'G = uZ : - - - 2e- Y - 1

Po

and after 2

zmm

: p2 -10.05

7

Y G i 8 - V z 5 = 2 e V - 1

Po is the starting polarisation measured just before the resonance line YG = uZ (Po = 0.9 f 0.01 in our experimental case at 880 MeV).

The maximum amplitude Zm

A

at 915 MeV is evaluated from initial amplitude at 5 MeV of 43,5 mm f 2 8m and a damping factor 4.06 which gives 10.56 Zmax 4 11.5 rnm.

Notice In experimental results the sign of polarisation after the

YG = 8 - ^{u z} resonance crossing is opposite to what we obtain straight forward in the computer due to a flip of the YG = 4 line of another nature not concerned here (efficiency - ^0.98) for the whole beam.

We have plotted polarisation versus Q (vertical axis is polarisa- tion after two lines crossing starting from 0.9), horizontal axis is intensity Q, normalised to one to make an easier comparison with experi- mental points ; (1 corresponds to almost 10 polarised protons 9

f 0.1.10 9 ).

Comments on the first results

We have two main parameters : maximum amplitudes inside the given limits and distribution of amplitudes inside the beam.

To enlarge the influence of amplitude dependance we have tried two values 9 mm and 12 mm quite unlikely, for both distributions Dl and D3.

It is not possible with these distribution to fit experimental data properly, but we can make general remarks.

For each case we have two figures : the first one with the true sign

of polarisation (figures a, b y c, d). In each figure one curve gives the

polarisation after Y G = u alone (for small intensity we have the effect

of core, only : polarisZation close to a positive maximum of 0.9 then

crosses zero for a larger Q and for maximum amplitude tends to - ^0.8), the

second curve gives polarisation after two resonances crossing ; it

starts also at 0.9 then decreases and with the same sign and increases

again for large amplitudes, to a higher level than the precedent one.

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The second figure gives the same curves but with an opposite sign for

Uz

case to make comparison with experimental points (figures a', b', cl,d').

a) polarisation after two resonances lines is always higher than after one.

A

b) maximum absolute value is larger when Zmax is larger (a' with bl, or c' with dl)

c) when we try uniform distribution Dl, difference between the two pola- risation curves is less marked : figures (a', b'),

d) with a denser core (D3) the two polarisation curves are separated but below experimental points figures (c' and dl).

To obtain a good fit, we need an amplitude of 11 mm and a distribu- tion richer in its core than the uniform one and a long uniform tail.

Distribution giving best results are of the form

A

D2 = k (m + (m - 1) cos ₎ if

A

Z ,< L and D2 = k if Z)L

The ratio L

= E

is for example 0.028 if rn = 2 and 0.014 if m = 3 ;

max

higher values of m do not change the results, figures I1 and 111.

CONCLUSION

With the chosen distribution, the fit is not too bad, and maximum amplitude 11 mm found is close to reality.

Probability of a dense core is high in the vertical plane for the Saturne I1 type of injection.

At that point, we need more experimental results to confirm all of this.

However, we have seen this type of phenomenon in the deceleration process where the polarisation measured after two crossings of the same line YG =

UZ

is slightly higher than expected (ref. 4).

REFERENCES

(1) Influence of betatron osci 1 lations on the proton beam polarisation, This conference,

A. NAKACH and al,

(2) Depolarisation d'un faisceau de protons polarises dans un synchrotron, Nuclear Instruments and Methods 2 (1960) (97-305)

M. FROISSART and R. STORA, (3) Resonances de depolarisation dans Saturne I1

GOC GERMA 75/48 - TP 28

E. GRORUD, JL. LACLARE, G. LELEUX,

(4) Determination of proton beam polarisation at high energies by measurements after deceleration

This conference,

J. BYSTRICKY and al.

(5)

JOURNAL DE PHYSIQUE

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COMPUTER SIMULATION OF THE VARIATION OF POLARISATION WITH EMITTANCE WHEN CROSSING TWO SUCCESSIVE INTRINSIC RESONANCES

HAL Id: jpa-00224601

https://hal.archives-ouvertes.fr/jpa-00224601

Submitted on 1 Jan 1985

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

COMPUTER SIMULATION OF THE VARIATION OF POLARISATION WITH EMITTANCE WHEN

CROSSING TWO SUCCESSIVE INTRINSIC RESONANCES

A. Nakach

To cite this version:

A. Nakach. COMPUTER SIMULATION OF THE VARIATION OF POLARISATION WITH EMIT-

TANCE WHEN CROSSING TWO SUCCESSIVE INTRINSIC RESONANCES. Journal de Physique

Colloques, 1985, 46 (C2), pp.C2-657-C2-662. �10.1051/jphyscol:1985282�. �jpa-00224601�

JOURNAL DE PHYSIQUE

Colloque C2, supplément au n°2, Tome 46, février 1985 page C2-657

COMPUTER SIMULATION OF THE VARIATION OF POLARISATION WITH EMITTANCE WHEN CROSSING TWO SUCCESSIVE INTRINSIC RESONANCES

A. Nakach

Laboratoire National Sattwne, CEN-Saclay, France

RESUME

Pour i n t e r p r ê t e r les r é s u l t a t s expérimentaux, précédemment d é c r i t s , une s i m u l a t i o n a été f a i t e sur c a l c u l a t e u r .

Plusieurs distributions des amplitudes d ' o s c i l l a t i o n à l ' i n t é r i e u r du faisceau ont été essayées. Une d i s t r i b u t i o n plus riche au centre reproduit assez bien l e s r é s u l t a t s trouvés.

ABSTRACT

Computer simulations have been done to understand experimental results concerning the increases of polarisation after crossing two successive intrinsic resonances (VG =

and FG = 8 - »

) .

Several distributions have been tried and a good agreement has been achieved with experimental curves.

INTRODUCTION

We recall fig. n° 1 experimental results concerning the variation of polarisation with the number of accelerated protons (ref. 1 ) , when we decrease vertical emittance by a closed orbit deformation which controls the loss of particles on a scraper.

Only those with the largest betatron amplitudes are lost.

These results can be understood if we admit existence of a core inside the beam, the polarisation of which is conserved through any resonances crossing of intrinsic type (at Saturne II VQ, = " at 915 MeV and FG = 8 -

at 1385 MeV) and peripheral particles with an adiabatic reversal of their spin, two times successively, restoring--- initial pola- risation (that of the core).

A computer simulation has bee^i done with several amplitudes distri- butions D (z) of the beam, its total size Z „ known and almost fixed.

' max Two extreme kinds of distributions have been tried. The uniform one

D i & = ^ a x a n d ™ e V*> = 1+4 1 ? r ^

\

max

max k is a normalisation coefficient such that

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985282

JOURNAL DE PHYSIQUE

We call :

Q = jZ D (:) dz

0 A

For one particle of amplitude Zmm the polarisation, following the Froissart and Stora formula (ref. 2 and 3) is given by, for Saturne I 1 ring

2 Zmm after Y'G = uZ : - - - 2e- Y - 1

Po

and after 2

zmm

: p2 -10.05

Y G i 8 - V z 5 = 2 e V - 1

Po is the starting polarisation measured just before the resonance line YG = uZ (Po = 0.9 f 0.01 in our experimental case at 880 MeV).

The maximum amplitude Zm

at 915 MeV is evaluated from initial amplitude at 5 MeV of 43,5 mm f 2 8m and a damping factor 4.06 which gives 10.56 Zmax 4 11.5 rnm.

Notice In experimental results the sign of polarisation after the

YG = 8 - u z resonance crossing is opposite to what we obtain straight forward in the computer due to a flip of the YG = 4 line of another nature not concerned here (efficiency - 0.98) for the whole beam.

We have plotted polarisation versus Q (vertical axis is polarisa- tion after two lines crossing starting from 0.9), horizontal axis is intensity Q, normalised to one to make an easier comparison with experi- mental points ; (1 corresponds to almost 10 polarised protons 9

f 0.1.10 9 ).

Comments on the first results

We have two main parameters : maximum amplitudes inside the given limits and distribution of amplitudes inside the beam.

To enlarge the influence of amplitude dependance we have tried two values 9 mm and 12 mm quite unlikely, for both distributions Dl and D3.

It is not possible with these distribution to fit experimental data properly, but we can make general remarks.

For each case we have two figures : the first one with the true sign

of polarisation (figures a, b y c, d). In each figure one curve gives the

polarisation after Y G = u alone (for small intensity we have the effect

of core, only : polarisZation close to a positive maximum of 0.9 then

crosses zero for a larger Q and for maximum amplitude tends to - 0.8), the

second curve gives polarisation after two resonances crossing ; it

starts also at 0.9 then decreases and with the same sign and increases

again for large amplitudes, to a higher level than the precedent one.

The second figure gives the same curves but with an opposite sign for

case to make comparison with experimental points (figures a', b', cl,d').

a) polarisation after two resonances lines is always higher than after one.

b) maximum absolute value is larger when Zmax is larger (a' with bl, or c' with dl)

c) when we try uniform distribution Dl, difference between the two pola- risation curves is less marked : figures (a', b'),

d) with a denser core (D3) the two polarisation curves are separated but below experimental points figures (c' and dl).

To obtain a good fit, we need an amplitude of 11 mm and a distribu- tion richer in its core than the uniform one and a long uniform tail.

Distribution giving best results are of the form

D2 = k (m + (m - 1) cos ) if

Z ,< L and D2 = k if Z)L

The ratio L

is for example 0.028 if rn = 2 and 0.014 if m = 3 ;

YG = 8 - ^{u z} resonance crossing is opposite to what we obtain straight forward in the computer due to a flip of the YG = 4 line of another nature not concerned here (efficiency - ^0.98) for the whole beam.

crosses zero for a larger Q and for maximum amplitude tends to - ^0.8), the

D2 = k (m + (m - 1) cos ₎ if