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Storage ring lattice design for a compact X-ray source
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 543 (2005) 78–80 www.elsevier.com/locate/nima
Storage ring lattice design for a compact X-ray source A.V. Poseryaev Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Vorob’evy Gory, Moscow 119992, Russian Federation Available online 25 February 2005
Abstract The lattice design of a compact storage ring for laser-electron X-ray generator at an energy 45 MeV is discussed. A quasi-monochromatic X-ray radiation is produced in the process of Compton backscattering of laser photons by counterpropagated relativistic electrons. Requirements to characteristics of the electron beam and lattice structure are formulated. The basic parameters of the storage ring are listed. r 2005 Elsevier B.V. All rights reserved. PACS: 29.20.Dh; 07.85.Fv; 29.27.Eg Keywords: Storage ring; Lattice structure; Chromaticity; Laser cooling
1. Introduction Nowadays the problem of construction of the compact X-ray source with a quasi-monochromatic spectrum is widely discussed [1–3]. One of the possible ways for its solution consists in the application of laser beam Compton backscattering on relativistic electrons. It is perspective to utilize multiple interaction of laser radiation stored in an optical resonator with electrons, circulating in a storage ring. In such a system, the effect of laser cooling allows one to receive a low emittance electron beam [1] which increases the efficiency of
light–electron interaction and opens up new possibilities for electron beam applications. We propose the lattice design of a compact storage ring to realize the scheme mentioned above.
2. Electron beam parameters The balance between the radiation damping and quantum excitation effects during the laser–electron interaction process determines the transversal emittances and relative energy spread of electron beam in the dispersion-free lattice structure [1]:
Corresponding author. Tel.: +7 095 9392451;
fax: +7 095 9395631. E-mail address: [email protected].
ðnx;z Þmin ¼
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.01.117
3 lc b 10 lL x;z
(1)
ARTICLE IN PRESS A.V. Poseryaev / Nuclear Instruments and Methods in Physics Research A 543 (2005) 78–80
ðsd Þmin
sffiffiffiffiffiffiffiffiffiffiffiffiffi 7 lc ¼ g 5 lL
(2)
where lc ¼ h=mc 2:43 1012 m is the Compton wavelength of the electron, lL is the laser wavelength, bx;z is the electron beta function (or the depth of focus) in the x or y direction at the laser–electron interaction region, and g ¼ E=mc2 ; E is the electron energy. For example, when 45 MeV electrons interact with lL 106 m wavelength laser and the depth of focus is bx;z 5 cm; the relative energy spread is ðsd Þmin 0:016 and the normalized transverse emittances are ðnx;z Þmin 3 108 mm mrad; which corresponds to the ffirms radius of the pffiffiffiffiffiffiffiffiffiffiffiffiffi electron beam sx;z ¼ bx;z x;z 3 mm: To achieve maximum interaction efficiency, the minimal transversal dimensions of the electron and laser beams should be equal in the interaction region. It is important to note that the intrabeam scattering effect can increase the values of transversal beam emittances.
3. Requirements to the parameters of the storage ring lattice structure
particles, and in particular high-order variations of betatron tune with momentum.
4. Storage ring lattice structure On the assumption of these conditions, we have proposed the scheme of a storage ring. The layout of the focusing structure elements as shown in Fig. 1. It consists of two long straight sections, four bending sections and two short straight sections. Each bending section includes three quadrupole lenses placed between two bending magnets BM. This configuration allows one to receive zero value of the dispersion function on the long straight sections and to solve a problem of natural chromaticity correction. It is possible to obtain a small enough value of the momentum compaction factor a by fitting of the quadrupole lens strength in the bending sections QBF and QBD, and short straight sections QD, which provides conditions for the electron beam circulation with the required relative energy spread sd ¼ 0:016 and relatively low accelerating cavity voltage V ¼ 2002300 kV: The reduction of the transversal beam dimensions in the interaction point IP is carried out by
To provide the maximum density of the electron beam in the region of its interaction with the photon beam, the following requirements must be fulfilled in this region:
βx
4
βz
zero value of the dispersion Dx, sufficiently low values of the electron beta functions bx;z 5 cm (low-b insertion), and the presence of only one low-b insertion with the high beam density (several low-b insertions with zero dispersion leads to an increase in the nonlinear Coulomb tune shift and magnifies the intrabeam scattering effects).
βx, βz, Dx, [m]
3
Dx
2 1 IP 0
BMBM
BM
BM
BM
BM BM
BM
-1 0
These requirements and the low degree of a storage ring symmetry inevitably lead to a number of undesirable side effects such as (a) high natural chromaticity, (b) high chromatic mismatch of the betatron envelope functions for off-momentum
79
2
4
6 S, [m]
8
10
Fig. 1. Layout of the storage ring. BM—bending magnets; QBF, QBD—quadrupoles of bending arc; QD—quadrupoles of short straight sections; QF2, QD3, QD4—quadrupoles of long straight injection section; QF1, QD1, QD2—quadrupoles of straight interaction section.
ARTICLE IN PRESS 80
A.V. Poseryaev / Nuclear Instruments and Methods in Physics Research A 543 (2005) 78–80
Table 1 Basic parameters of the storage ring Parameter
Value
Operating energy (MeV) Circumference (m) Tunes Horizontal, Qx Vertical, Qz Amplitude functions at IP (cm) Horizontal, bx Vertical, bz RF voltage amplitude (kV) RF frequency (MHz) Harmonic number, q Momentum compaction factor, a Synchrotron oscillation tune, Qs Energy acceptance (%) Natural chromaticity Horizontal, Q=x Vertical, Q=z
45 11.55
is large enough for the location of accelerating cavities and injection system. The basic parameters of the storage ring are given in Table 1. Fig. 2 shows horizontal bx and vertical bz amplitude functions and dispersion function Dx.
4.290 2.633 5 5 300 571.2 22 0.008 0.014 715 8.314 7.700
5. Conclusion We propose the lattice structure of the electron storage ring. The facility can provide highintensity quasi-monochromatic X-ray radiation based on the laser beam Compton backscattering on relativistic electrons. It also permits one to research the process of laser cooling and the effect of intrabeam scattering.
Acknowledgements The author thanks V.I. Shvedunov and E.G. Bessonov for many useful discussions. References
Fig. 2. Lattice focusing functions.
means of strong quadrupole triplet QD1, QF1, QD2. The length of the straight section free parts
[1] Z. Huang, R. Ruth, Phys. Rev. Lett. 80 (1998) 976. [2] E.G. Bessonov, R.M. Fechtchenko, M.V. Gorbunkov, V.I. Shvedunov, A.V. Vinogradov, ICXRL Proceedings, Chinese Republic, 2004. [3] P. Gladkikh, et al., Proceedings of EPAC 2000, Austria, vol. 1, p. 696.
Nuclear Instruments and Methods in Physics Research A 543 (2005) 78–80 www.elsevier.com/locate/nima
Storage ring lattice design for a compact X-ray source A.V. Poseryaev Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Vorob’evy Gory, Moscow 119992, Russian Federation Available online 25 February 2005
Abstract The lattice design of a compact storage ring for laser-electron X-ray generator at an energy 45 MeV is discussed. A quasi-monochromatic X-ray radiation is produced in the process of Compton backscattering of laser photons by counterpropagated relativistic electrons. Requirements to characteristics of the electron beam and lattice structure are formulated. The basic parameters of the storage ring are listed. r 2005 Elsevier B.V. All rights reserved. PACS: 29.20.Dh; 07.85.Fv; 29.27.Eg Keywords: Storage ring; Lattice structure; Chromaticity; Laser cooling
1. Introduction Nowadays the problem of construction of the compact X-ray source with a quasi-monochromatic spectrum is widely discussed [1–3]. One of the possible ways for its solution consists in the application of laser beam Compton backscattering on relativistic electrons. It is perspective to utilize multiple interaction of laser radiation stored in an optical resonator with electrons, circulating in a storage ring. In such a system, the effect of laser cooling allows one to receive a low emittance electron beam [1] which increases the efficiency of
light–electron interaction and opens up new possibilities for electron beam applications. We propose the lattice design of a compact storage ring to realize the scheme mentioned above.
2. Electron beam parameters The balance between the radiation damping and quantum excitation effects during the laser–electron interaction process determines the transversal emittances and relative energy spread of electron beam in the dispersion-free lattice structure [1]:
Corresponding author. Tel.: +7 095 9392451;
fax: +7 095 9395631. E-mail address: [email protected].
ðnx;z Þmin ¼
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.01.117
3 lc b 10 lL x;z
(1)
ARTICLE IN PRESS A.V. Poseryaev / Nuclear Instruments and Methods in Physics Research A 543 (2005) 78–80
ðsd Þmin
sffiffiffiffiffiffiffiffiffiffiffiffiffi 7 lc ¼ g 5 lL
(2)
where lc ¼ h=mc 2:43 1012 m is the Compton wavelength of the electron, lL is the laser wavelength, bx;z is the electron beta function (or the depth of focus) in the x or y direction at the laser–electron interaction region, and g ¼ E=mc2 ; E is the electron energy. For example, when 45 MeV electrons interact with lL 106 m wavelength laser and the depth of focus is bx;z 5 cm; the relative energy spread is ðsd Þmin 0:016 and the normalized transverse emittances are ðnx;z Þmin 3 108 mm mrad; which corresponds to the ffirms radius of the pffiffiffiffiffiffiffiffiffiffiffiffiffi electron beam sx;z ¼ bx;z x;z 3 mm: To achieve maximum interaction efficiency, the minimal transversal dimensions of the electron and laser beams should be equal in the interaction region. It is important to note that the intrabeam scattering effect can increase the values of transversal beam emittances.
3. Requirements to the parameters of the storage ring lattice structure
particles, and in particular high-order variations of betatron tune with momentum.
4. Storage ring lattice structure On the assumption of these conditions, we have proposed the scheme of a storage ring. The layout of the focusing structure elements as shown in Fig. 1. It consists of two long straight sections, four bending sections and two short straight sections. Each bending section includes three quadrupole lenses placed between two bending magnets BM. This configuration allows one to receive zero value of the dispersion function on the long straight sections and to solve a problem of natural chromaticity correction. It is possible to obtain a small enough value of the momentum compaction factor a by fitting of the quadrupole lens strength in the bending sections QBF and QBD, and short straight sections QD, which provides conditions for the electron beam circulation with the required relative energy spread sd ¼ 0:016 and relatively low accelerating cavity voltage V ¼ 2002300 kV: The reduction of the transversal beam dimensions in the interaction point IP is carried out by
To provide the maximum density of the electron beam in the region of its interaction with the photon beam, the following requirements must be fulfilled in this region:
βx
4
βz
zero value of the dispersion Dx, sufficiently low values of the electron beta functions bx;z 5 cm (low-b insertion), and the presence of only one low-b insertion with the high beam density (several low-b insertions with zero dispersion leads to an increase in the nonlinear Coulomb tune shift and magnifies the intrabeam scattering effects).
βx, βz, Dx, [m]
3
Dx
2 1 IP 0
BMBM
BM
BM
BM
BM BM
BM
-1 0
These requirements and the low degree of a storage ring symmetry inevitably lead to a number of undesirable side effects such as (a) high natural chromaticity, (b) high chromatic mismatch of the betatron envelope functions for off-momentum
79
2
4
6 S, [m]
8
10
Fig. 1. Layout of the storage ring. BM—bending magnets; QBF, QBD—quadrupoles of bending arc; QD—quadrupoles of short straight sections; QF2, QD3, QD4—quadrupoles of long straight injection section; QF1, QD1, QD2—quadrupoles of straight interaction section.
ARTICLE IN PRESS 80
A.V. Poseryaev / Nuclear Instruments and Methods in Physics Research A 543 (2005) 78–80
Table 1 Basic parameters of the storage ring Parameter
Value
Operating energy (MeV) Circumference (m) Tunes Horizontal, Qx Vertical, Qz Amplitude functions at IP (cm) Horizontal, bx Vertical, bz RF voltage amplitude (kV) RF frequency (MHz) Harmonic number, q Momentum compaction factor, a Synchrotron oscillation tune, Qs Energy acceptance (%) Natural chromaticity Horizontal, Q=x Vertical, Q=z
45 11.55
is large enough for the location of accelerating cavities and injection system. The basic parameters of the storage ring are given in Table 1. Fig. 2 shows horizontal bx and vertical bz amplitude functions and dispersion function Dx.
4.290 2.633 5 5 300 571.2 22 0.008 0.014 715 8.314 7.700
5. Conclusion We propose the lattice structure of the electron storage ring. The facility can provide highintensity quasi-monochromatic X-ray radiation based on the laser beam Compton backscattering on relativistic electrons. It also permits one to research the process of laser cooling and the effect of intrabeam scattering.
Acknowledgements The author thanks V.I. Shvedunov and E.G. Bessonov for many useful discussions. References
Fig. 2. Lattice focusing functions.
means of strong quadrupole triplet QD1, QF1, QD2. The length of the straight section free parts
[1] Z. Huang, R. Ruth, Phys. Rev. Lett. 80 (1998) 976. [2] E.G. Bessonov, R.M. Fechtchenko, M.V. Gorbunkov, V.I. Shvedunov, A.V. Vinogradov, ICXRL Proceedings, Chinese Republic, 2004. [3] P. Gladkikh, et al., Proceedings of EPAC 2000, Austria, vol. 1, p. 696.