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A new method for mass measurements at the storage ring
NUCLEAR
PHYSICS A Nuclear Physics A626 (1997) 333c-336c
ELSEVIER
A new method for mass measurements at the storage ring N.I. Tarantin Joint Institute for Nuclear Research, Dubna, Moscow Region 141980, Russia
It is proposed to use ion momentum selection in the storage ring to improve the precision of mass measurements.
1. INTRODUCTION Data on nuclear masses provide the basis for creating and testing various nuclear models. Determining the bending energy, the masses of nuclei reflect the balance between the nuclear and Coulomb forces, and a knowledge about their values is of great importance for the configuration of the nucleons in nuclei to be established. To compare theoretical models with measured results is of special interest for short-lived nuclei far from the beta-stability line.
2. STORAGE R I N G AS A MASS SPECTROMETER Under a certain condition a storage ring is a good tool for highly precise nuclear mass measurements. A mass measurement method proposed in [1] is based on the analysis of the revolution frequencies of the stored ions preliminary cooled by electrons. The Schottky spectral lines of the ions stored and cooled in the ring become very narrow, the property that permits measuring the masses of ions with a precision of 10"6 order. For ion mass measurements, we proposed a method based on the momentum selection of the ions circulating in the storage ring. The selection is performed by a superconducting solenoid in order to improve the resolution and precision while measuring the masses of ions at a storage ring. This method was first reported in the form of abstracts [2] and presented by a talk at the Second International Symposium on Nuclear Physics at Storage Rings.
3. PRINCIPLES OF THE MASS MEASUREMENTS AT THE STORAGE RING The revolution frequency, f, of the ions moving in a magnetic field is determined by the simple formula: 2~
f =~
1 I; (~p,r, z)d~o
(1)
o 0375-9474/98/$19.00 © 1998 Elsevier Science B.k( Pll S0375-9474(97)00554-X
All rights reserved.
334c
N.L Tarantin/Nuclear Physics A626 (1997) 333c 336c
where c,o is the angular ion velocity, r and z are the radial and axial coordinates of the ion. The charged particle's velocity, v, being constant in the magnetic field, then within linear approach ~o=(vo/Ro)(1-p+Sv)
(2)
where Ro is the radius of the optical axis, p=p(q~)=[r(q))-R0]/Ro is the relative radial coordinate of the charge particle trajectory, 8v=(v-v0)/v0=Av/v0 is the random spread of the charged particle velocities in the beam. We express p(q~) with the linear solution of the trajectory equation in an axial symmetric magnetic field Bz=Bo(l+blp+...) depending only on the parameter 8=Am/m0+Av/v0-Aq/q0, where m, v and q are the ion's dynamic mass, velocity and charge, p~(cp)=(1/p2)(1-cospq~)8
(3)
where p2=(l+b). We drop the corresponding linear solutions depending on the initial coordinate p(0) and its derivative Op(0)/&~ taking account of either small contribution of ion transverse emittance or the geometrical isochronous mode motion. It follows from (1-3) that the relative difference of the revolution frequencies of two particles 8f=Af/fo=[1-(yo/p)Z(1-sin27tp/2~p)]8v-(1/p2)(1-sin27tp/27tp)(Smrost-fq)
(4)
where Y0 is the relativistic Lorentz factor of the particle, mre~tis the particle's rest mass. It follows from (4) that the charged particle's frequency in an axial symmetric magnetic field doesn't depend on its velocity provided l-(y0/p)Z(1-sin27tp/27tp)=0
(s)
The condition (5) is obeyed by nonrelativistic particles (70=1) and in an uniform magnetic field (b~=0, p=l). For y0>l condition (5) requires p>l, i.e. bl>0, that leads to the defocusing of charged particles in such magnetic field because axial restoring force ~(-b0 v2. The magnetic field in the storage ring being of periodic structure, the value p is replaced by the number of betatron oscillations of the charged particles in the radial plane per one revolution Qr. It should be noted that in storage ring with Qr>0 the value Qz is also made positive where Qz is similar to Qr for axial motion. In this case the value Q,/[1sin2rtQ,/2rtQr] v2 similar to p/(1-sin27tp/2np) v2 in (5) is denoted 7t~ (transition), and equation (4) is transformed into
8f=-(l -yo2/yt~2)Sv-(1/yf)(Smro~,- 8q)
(6)
It follows from equation (6) that, the first term minimized, the storage ring can be used for precise mass measurement. A possible way is to provide the very small values of Sv by using an electron cooling facility. Another way requires that the storage ring should be tuned to realize the 7trvalue equal to the 70-value for the stored charged particles [3]. Unfortunately,
335c
N.I. Tarantin/Nuclear Physics A626 (1997) 333c-336c
the momentum acceptance of a storage ring decreases strongly with decreasing 7u. The significance of Tu and Y0being comparing in value is shown, for example, in work [4] entitled "New Calculations for the Isochronous Mode of the ESR - toward direct mass measurement of exotic nuclei" and in work [5]. The technical proposal on the storage ring K4-KI0 [6] doesn't deal with the problem concerning the equality "&=70, and the K10 storage ring has Tu=5.26 and 70~2. These values not comparing in value doesn't allow precise measurements by methods of electron cooling.
4. NEW METHOD FOR THE MASS MEASUREMENTS ON THE STORAGE RING
The formula (6) expressed d v : ( l / y ~ ) f i m .... + (l/702)b'P gives
through
8f=-(l/yu2- I/y02)SP-(I/T02)Sm~,t+(l/7~2)8q
the
charge
particles
momentum
P
(7)
where 8P=AP/P0. Equations (7) shows a new possible way for mass measurement on the storage ring by means of the magnetic momentum selection of the ions. The main features of the method are the following. The ion momentum selection decreases or excludes the chromatic beam aberrations of the ions moving in the magnetic field of the storage ring. The ion momentum selection decreases the intensity of the interference ions and thus decreases interbeam ion scattering. The ion momentum selection increases the mass dispersion coefficient of the ions by a factor of (7u/70)2 (see formulas (7) and (6), usually )'w-~'0). The ion momentum selection by a superconducting solenoid gives 8P
5. REALIZATION OF THE METHOD The ion momentum selection is performed by a superconducting solenoid located in the straight -line section and displaced relative to the optical axis of the storage ring. Taking into account the fringing field effect at the solenoid boundaries [7], the radial and azimuthal coordinates of the trajectories of the ions moving in the magnetic solenoid field were considered. The radial projection of the ion trajectory of P0 momentum (y2=y~) is shown in Figure 1 at the condition KoL[l+(rtyl/L)2]vz=7~, where K0=q0B0/2P0, L is effective length of solenoid. The trajectories of the ions of Po+AP momentum are additionally described by the geometric-chromatic second order aberration members Ay and Aot=2rtylKoSP. The solenoid displaced from the storage ring's optical axis (from the dashed line) by yl~L/27t 2, the aberration Ac~ becomes an essentially great value Aet~SP.
336c
NI. Tarantin/Nuclear Physics A626 (1997) 333c-336c
y~
,t
X P
B
I
L
<. ,q
Figure 1. The radial projection of the ion trajectories in the solenoid.
Figure 2 shows the result of the solenoid action in the storage ring. Here one can see one initially unresolved (after the electron cooling) lines in the frequency revolution spectrum and two resolved lines (after the momentum selection by the solenoid) in the frequency distribution. It follows from experience of using a superconducting solenoid that a mass resolution of about 10"s can be obtained by the proposed method.
A f ~ dP
A f ~ dv
f
Figure 2. The result of the solenoid performance in the storage ring.
REFERENCES
1. B.Franzke, Nucl. Instr. and Meth. B24/25 (1987) 18. 2. N.I.Tarantin, Abstracts "The second International Symposium on Nuclear Physics at Storage Rings", St.-Petersburg, Russia, May 16-21 (1994) 8; J1NR FLNR "Scientific Report 1993-1994," Dubna (1995) 205. 3. J.Trotscher et al., Nucl. Instr. and Meth. B70 (1992) 455. 4. Y.Fujita et al., "GSI Scientific Report 1992", 93-1, Darmstadt (1993) 369. 5. B.Franzke et al., "GSI Scientific Report 193", 94-1, Darmstadt (1994) 305. 6. V.V.Parhomchuk et al., In: "Heavy ion storage ring complex K4-K10" A technical proposal (Ed. G.M.Ter-Akopian), JINR E-9-92-75, Dubna (1992) 38. 7. N.I.Tarantin. "Magnetic Static Analyzers of Charged Particles. Fields and linear Optics". 1986, Energoatomizdat, Moscow (in Russian).
PHYSICS A Nuclear Physics A626 (1997) 333c-336c
ELSEVIER
A new method for mass measurements at the storage ring N.I. Tarantin Joint Institute for Nuclear Research, Dubna, Moscow Region 141980, Russia
It is proposed to use ion momentum selection in the storage ring to improve the precision of mass measurements.
1. INTRODUCTION Data on nuclear masses provide the basis for creating and testing various nuclear models. Determining the bending energy, the masses of nuclei reflect the balance between the nuclear and Coulomb forces, and a knowledge about their values is of great importance for the configuration of the nucleons in nuclei to be established. To compare theoretical models with measured results is of special interest for short-lived nuclei far from the beta-stability line.
2. STORAGE R I N G AS A MASS SPECTROMETER Under a certain condition a storage ring is a good tool for highly precise nuclear mass measurements. A mass measurement method proposed in [1] is based on the analysis of the revolution frequencies of the stored ions preliminary cooled by electrons. The Schottky spectral lines of the ions stored and cooled in the ring become very narrow, the property that permits measuring the masses of ions with a precision of 10"6 order. For ion mass measurements, we proposed a method based on the momentum selection of the ions circulating in the storage ring. The selection is performed by a superconducting solenoid in order to improve the resolution and precision while measuring the masses of ions at a storage ring. This method was first reported in the form of abstracts [2] and presented by a talk at the Second International Symposium on Nuclear Physics at Storage Rings.
3. PRINCIPLES OF THE MASS MEASUREMENTS AT THE STORAGE RING The revolution frequency, f, of the ions moving in a magnetic field is determined by the simple formula: 2~
f =~
1 I; (~p,r, z)d~o
(1)
o 0375-9474/98/$19.00 © 1998 Elsevier Science B.k( Pll S0375-9474(97)00554-X
All rights reserved.
334c
N.L Tarantin/Nuclear Physics A626 (1997) 333c 336c
where c,o is the angular ion velocity, r and z are the radial and axial coordinates of the ion. The charged particle's velocity, v, being constant in the magnetic field, then within linear approach ~o=(vo/Ro)(1-p+Sv)
(2)
where Ro is the radius of the optical axis, p=p(q~)=[r(q))-R0]/Ro is the relative radial coordinate of the charge particle trajectory, 8v=(v-v0)/v0=Av/v0 is the random spread of the charged particle velocities in the beam. We express p(q~) with the linear solution of the trajectory equation in an axial symmetric magnetic field Bz=Bo(l+blp+...) depending only on the parameter 8=Am/m0+Av/v0-Aq/q0, where m, v and q are the ion's dynamic mass, velocity and charge, p~(cp)=(1/p2)(1-cospq~)8
(3)
where p2=(l+b). We drop the corresponding linear solutions depending on the initial coordinate p(0) and its derivative Op(0)/&~ taking account of either small contribution of ion transverse emittance or the geometrical isochronous mode motion. It follows from (1-3) that the relative difference of the revolution frequencies of two particles 8f=Af/fo=[1-(yo/p)Z(1-sin27tp/2~p)]8v-(1/p2)(1-sin27tp/27tp)(Smrost-fq)
(4)
where Y0 is the relativistic Lorentz factor of the particle, mre~tis the particle's rest mass. It follows from (4) that the charged particle's frequency in an axial symmetric magnetic field doesn't depend on its velocity provided l-(y0/p)Z(1-sin27tp/27tp)=0
(s)
The condition (5) is obeyed by nonrelativistic particles (70=1) and in an uniform magnetic field (b~=0, p=l). For y0>l condition (5) requires p>l, i.e. bl>0, that leads to the defocusing of charged particles in such magnetic field because axial restoring force ~(-b0 v2. The magnetic field in the storage ring being of periodic structure, the value p is replaced by the number of betatron oscillations of the charged particles in the radial plane per one revolution Qr. It should be noted that in storage ring with Qr>0 the value Qz is also made positive where Qz is similar to Qr for axial motion. In this case the value Q,/[1sin2rtQ,/2rtQr] v2 similar to p/(1-sin27tp/2np) v2 in (5) is denoted 7t~ (transition), and equation (4) is transformed into
8f=-(l -yo2/yt~2)Sv-(1/yf)(Smro~,- 8q)
(6)
It follows from equation (6) that, the first term minimized, the storage ring can be used for precise mass measurement. A possible way is to provide the very small values of Sv by using an electron cooling facility. Another way requires that the storage ring should be tuned to realize the 7trvalue equal to the 70-value for the stored charged particles [3]. Unfortunately,
335c
N.I. Tarantin/Nuclear Physics A626 (1997) 333c-336c
the momentum acceptance of a storage ring decreases strongly with decreasing 7u. The significance of Tu and Y0being comparing in value is shown, for example, in work [4] entitled "New Calculations for the Isochronous Mode of the ESR - toward direct mass measurement of exotic nuclei" and in work [5]. The technical proposal on the storage ring K4-KI0 [6] doesn't deal with the problem concerning the equality "&=70, and the K10 storage ring has Tu=5.26 and 70~2. These values not comparing in value doesn't allow precise measurements by methods of electron cooling.
4. NEW METHOD FOR THE MASS MEASUREMENTS ON THE STORAGE RING
The formula (6) expressed d v : ( l / y ~ ) f i m .... + (l/702)b'P gives
through
8f=-(l/yu2- I/y02)SP-(I/T02)Sm~,t+(l/7~2)8q
the
charge
particles
momentum
P
(7)
where 8P=AP/P0. Equations (7) shows a new possible way for mass measurement on the storage ring by means of the magnetic momentum selection of the ions. The main features of the method are the following. The ion momentum selection decreases or excludes the chromatic beam aberrations of the ions moving in the magnetic field of the storage ring. The ion momentum selection decreases the intensity of the interference ions and thus decreases interbeam ion scattering. The ion momentum selection increases the mass dispersion coefficient of the ions by a factor of (7u/70)2 (see formulas (7) and (6), usually )'w-~'0). The ion momentum selection by a superconducting solenoid gives 8P
5. REALIZATION OF THE METHOD The ion momentum selection is performed by a superconducting solenoid located in the straight -line section and displaced relative to the optical axis of the storage ring. Taking into account the fringing field effect at the solenoid boundaries [7], the radial and azimuthal coordinates of the trajectories of the ions moving in the magnetic solenoid field were considered. The radial projection of the ion trajectory of P0 momentum (y2=y~) is shown in Figure 1 at the condition KoL[l+(rtyl/L)2]vz=7~, where K0=q0B0/2P0, L is effective length of solenoid. The trajectories of the ions of Po+AP momentum are additionally described by the geometric-chromatic second order aberration members Ay and Aot=2rtylKoSP. The solenoid displaced from the storage ring's optical axis (from the dashed line) by yl~L/27t 2, the aberration Ac~ becomes an essentially great value Aet~SP.
336c
NI. Tarantin/Nuclear Physics A626 (1997) 333c-336c
y~
,t
X P
B
I
L
<. ,q
Figure 1. The radial projection of the ion trajectories in the solenoid.
Figure 2 shows the result of the solenoid action in the storage ring. Here one can see one initially unresolved (after the electron cooling) lines in the frequency revolution spectrum and two resolved lines (after the momentum selection by the solenoid) in the frequency distribution. It follows from experience of using a superconducting solenoid that a mass resolution of about 10"s can be obtained by the proposed method.
A f ~ dP
A f ~ dv
f
Figure 2. The result of the solenoid performance in the storage ring.
REFERENCES
1. B.Franzke, Nucl. Instr. and Meth. B24/25 (1987) 18. 2. N.I.Tarantin, Abstracts "The second International Symposium on Nuclear Physics at Storage Rings", St.-Petersburg, Russia, May 16-21 (1994) 8; J1NR FLNR "Scientific Report 1993-1994," Dubna (1995) 205. 3. J.Trotscher et al., Nucl. Instr. and Meth. B70 (1992) 455. 4. Y.Fujita et al., "GSI Scientific Report 1992", 93-1, Darmstadt (1993) 369. 5. B.Franzke et al., "GSI Scientific Report 193", 94-1, Darmstadt (1994) 305. 6. V.V.Parhomchuk et al., In: "Heavy ion storage ring complex K4-K10" A technical proposal (Ed. G.M.Ter-Akopian), JINR E-9-92-75, Dubna (1992) 38. 7. N.I.Tarantin. "Magnetic Static Analyzers of Charged Particles. Fields and linear Optics". 1986, Energoatomizdat, Moscow (in Russian).