Single-shot measurement of longitudinal phase space beam profile in an electron storage ring

Kim, J.; Jang, G.S.; Oh, B.H.; Lee, J.; Shin, S.

doi:10.1107/S1600577521011127

research papers

JOURNAL OF
SYNCHROTRON
RADIATION

ISSN: 1600-5775

Volume 29| Part 1| January 2022| Pages 111-117

https://doi.org/10.1107/S1600577521011127

Open

access

Single-shot measurement of longitudinal phase space beam profile in an electron storage ring

J. Kim,^a G. S. Jang,^b B. H. Oh,^c J. Lee ^c and S. Shin ^c ^*

^aSLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA, ^bDepartment of Physics, POSTECH, Pohang, Gyungbuk 37673, Republic of Korea, and ^cPohang Accelerator Laboratory, POSTECH, Pohang, Gyungbuk 37673, Republic of Korea
^*Correspondence e-mail: tlssh@postech.ac.kr

Edited by A. Stevenson, Australian Synchrotron, Australia (Received 16 March 2021; accepted 23 October 2021)

A novel scheme to measure the longitudinal emittance and phase space profile in an electron storage ring by using correlations between time and the vertical coordinate, and between energy and the horizontal coordinate, is proposed. This longitudinal profile measurement scheme will help to demonstrate recent results of advanced studies for manipulating the longitudinal beam profile and for investigating beam instability in an electron storage ring.

Keywords: longitudinal emittance; phase space profile; storage ring.

1. Introduction

Transverse bunch crabbing using a two-frequency crab cavity scheme (Zholents, 2015 ; Huang et al., 2019 ) provides the optimal solution to produce short-pulse (1–10 ps full width at half-maximum) X-rays in a storage ring. This scheme would enable increased precision of timing-mode studies of a large number of dynamic processes in materials as they function. A crab cavity can also be used as an injection kicker in a new on-axis injection scheme (Kim et al., 2019 ) that uses a transverse deflecting radio-frequency (RF) cavity to kick the incoming beam into an already populated bucket but with a timing offset from the synchronous phase.

A crab cavity can also be used to measure bunch length (Loew & Altenmueller, 1965 ; Emma et al., 2000 ). A crab cavity couples the y–z or x–z planes, so bunch length is projected in the y or x dimension, respectively. The resolution of this bunch length measurement is limited by transverse emittances ɛ_x and ɛ_y unless a specialized beam transport line such as a chicane (Xiang & Ding, 2010 ) is used. Regardless of using a crab cavity, the distribution of the energy deviation $[\delta]$ = #!dp/p of a bunch can be projected in the x dimension at which horizontal dispersion η_x is large. The resolution of this is limited by the ratio ɛ_x/η_x. Combining these two principles enables measurement of the longitudinal profiles (z–δ) of a bunch in the x–y plane.

A fourth-generation storage ring (4GSR) is an accelerator that provides small emittance so that the measurement can be made with high resolution. A 4GSR adopts a multi-bend achromat (MBA), that effectively suppresses natural emittance. The MAX IV 4GSR is currently operating; others, including APS-U, SPring-8-II, SLS-II, ALS-U, SIRIUS, ESRF-EBS and Korea-4GSR, are being designed, constructed or commissioned [Streun, 2017 ; Steier et al., 2016 ; Liu et al., 2013 ; see also design reports for MAX IV (https://www.maxiv.lu.se/acceleratorsbeamlines/accelerators/acceleratordocumentation/max-iv-ddr), APS Upgrade (https://www.aps.anl.gov/APSUpgrade), SPring-8-II (http://rsc.riken.jp/eng/index.html) and ESRF-EBS (https://indico.psi.ch/event/5589/)]. All of these rings use the MBA concept. A single cell of an MBA lattice has M-1 dispersion maxima with similar amplitudes, and one of these maxima can be used as a watching point for the measurement using a crab cavity. A hybrid MBA lattice such as APS-U, ESRF-EBS or Korea-4GSR provides two large dispersion bumps at the edge of a cell to enable effective correction of chromaticity, and the region of the large dispersion bumps is a desirable choice as a watching point.

In this study, we show that in a storage ring that uses a hybrid MBA lattice the measurement on longitudinal bunch profiles gives good resolution without the need for other additional magnets. In Section 2, we recall the matrix formalism between two arbitrary points of a storage ring, and projection of longitudinal (z–δ) beam profiles on the transverse (x–y) plane by using a crab cavity. In Section 3, we briefly introduce PAL-4GSR, which is used as an example lattice for the novel measurement scheme. We also calculated the intrinsic resolution of the measurement in PAL-4GSR. In Section 4, we present a numerical simulation of the measurement of the longitudinal profile by using the PAL-4GSR lattice. We also examine the resolution of the measurement when wakefield data are included.

2. Coupling of the y–z plane

Projection of the z–δ beam profile into the x–y plane can be described by linear optics theory. A thin crab cavity of TM110 mode has a linearized function as follows (Huang, 2016 ),

$[T_{\rm{c}} = \left( \matrix{1& 0& 0& 0& 0& 0\cr 0& 1& 0& 0& 0& 0\cr 0& 0& 1& 0& 0& 0\cr 0& 0& 0& 1& \epsilon & 0\cr 0& 0& 0& 0& 1& 0\cr 0& 0& \epsilon & 0& 0& 1}\right), \eqno(1)]$

where ε = #!eVk/E₀, in which e is the electron charge, V [V] is the maximum voltage of a crab cavity, k is the angular wavenumber and E₀ [eV] is the nominal energy of a beam. In a storage ring, a linear matrix from arbitrary position 1 to arbitrary position 2 is given as (Chao, 2002 )

$[{M}_{12} = \left(\matrix{{R}_{11}& {R}_{12}& 0& 0& 0& {\eta }_{2}-{R}_{11}{\eta }_{1}-{R}_{12}\eta^{\prime}_{1}\cr {R}_{21}& {R}_{22}& 0& 0& 0& \eta^{\prime}_{2}-{R}_{21}{\eta }_{1}-{R}_{22}\eta^{\prime}_{1}\cr 0& 0& {R}_{33}& {R}_{34}& 0& 0\cr 0& 0& {R}_{43}& {R}_{44}& 0& 0\cr A& B& 0& 0& 1& C-A{\eta }_{1}-B\eta^{\prime}_{1}\cr 0& 0& 0& 0& 0& 1}\right). \eqno(2)]$

Definitions of each matrix element can be found in Appendix A. When initial beam coordinates at the position 1 are given as X₁ = (x₁, $[x_1^{\prime}]$ , y₁, $[y_1^{\prime}]$ , z₁, δ₁), its continuous mapping via T_c and M₁₂ becomes

$[\eqalignno{ X_2 & = M_{12}T_{\rm{c}}X_1 = \left( \matrix{ \eqalign{ R_{11}x_1 & + R_{12}x_1^{\,\prime} \cr& + (\eta_2 - R_{11}\eta_1 - R_{12}\eta_1^{\,\prime})\,y_1\epsilon \cr& + (\eta_2 - R_{11}\eta_1 - R_{12}\eta_1^{\,\prime})\,\delta_1 } \cr\cr \eqalign{ R_{21}x_1 & + R_{22}x_1^{\,\prime} \cr& + (\eta_2^{\prime} - R_{21}\eta_1 - R_{22}\eta_1^{\,\prime})\,y_1\epsilon \cr& + (\eta_2^{\,\prime} - R_{21}\eta_1 - R_{22}\eta_1^{\,\prime})\,\delta_1 } \cr \,\,R_{33}y_1 + R_{34}\,y_1^{\prime} + R_{34\,}z_1\epsilon\vphantom{\bigg|} \hfill \cr \,\,R_{43}y_1 + R_{44}\,y_1^{\prime} + R_{44\,}z_1\epsilon\vphantom{_\big|} \hfill \cr \eqalign{ \,Ax_1 + Bx_1^{\,\prime} & + (C-A\eta_1 - B\eta_1^{\,\prime})\,y_1\epsilon \cr& + (C-A\eta_1 - B\eta_1^{\,\prime})\,\delta_1} \cr \,\,y_1\epsilon+\delta_1 \hfill } \right). & (3)}]$

Let us assume that position 1 is located at one of the achromats of a storage ring (η₁ = 0), and position 2 is at a point that has large dispersion. If ψ_x ≃ (2n + 1)π and ψ_y ≃ $[[{{(2n+1)}/{2}}]\,\pi]$ , contributions from R₁₂ and R₃₃ are negligible. The magnitude of R₁₁ is approximately $[({{{{\beta_{x2}}}/{{\beta_{x1}}}}})^{1/2}]$ when ψ_x ≃ (2n + 1)π, and it is conservatively less than 3 as the ratio of β_x2 over β_x1 is less than 10 for most lattices. Specifically, when emittance ≃ 100 pm, δ₁ ≃ 0.001 and η₂ ≃ 0.10 m, the contribution from $[{\eta_2}{\sigma_{{\delta_1}}}]$ at x₂ is one order larger than that from $[{\sigma_{{x_1}}}]$ (i.e. $[{\sigma_{{x_1}}}]$ ≃ 10⁻⁵ m and $[{\eta_2}{\sigma_{{\delta _1}}}]$ ≃ 10⁻⁴), which means we can expect projection between x₂ and $[{\eta_2}{\sigma_{{\delta_1}}}]$ . Likewise, y₂ is dominated by R₃₄z₁ε as $[{\sigma_{y_1^{\,\prime}}}]$ is of the order of 10⁻⁶ but z₁ is of the order of 10⁻³ and ε has order 10⁻². Clearly, smaller emittance will lead to better resolution.

Hence, x and y coordinates at position 2 are expressed as

$[\left({\matrix{ {{x_2}} \cr {{y_2}} \cr } } \right) \,\cong\, \left(\matrix{0& {\eta }_{2}\cr {R}_{34}\epsilon & 0}\right)\left(\matrix{{z}_{1}\cr {\delta }_{1}}\right), \eqno(4)]$

which shows the projection of the z–δ plane onto the x–y plane. Its resolution is mainly dependent on whether the contributions from x₁, $[x_1^{\prime}]$ , y₁ and $[y_1^{\prime}]$ are negligible and whether ψ_x ≃ (2n + 1)π and ψ_y ≃ $[[{{(2n+1)}/{2}}]\,\pi]$ . If they are, then R₃₄ has sin(ψ_y) dependence, so large η₂ leads to increased magnification for the x plane, and ψ_y close to $[[{{({2n+1})}/2}]\,{{\pi}}]$ leads to increased magnification for the y plane.

A hybrid MBA lattice such as ESRF-EBS, APS-U, PAL-4GSR satisfies the above-described conditions. Due to the common (ψ_x, ψ_y) = (3π, π) phase advance between two dispersion bumps in a cell of a hybrid MBA lattice, each cell has a similar phase advance. Specifically, a hybrid MBA lattice has φ_x ≃ 0.9π and φ_y ≃ 0.4π from the center of the long straight section to the nearest dispersion bump. Hence, choosing the position of a crab cavity satisfying φ_y = $[{{\pi}/{2}}]$ is accompanied by φ_x ≃ π.

3. PAL-4GSR and the intrinsic resolution

The PAL-4GSR storage ring is a hybrid seven-bend achromat (H7BA) lattice with a horizontal emittance of 90 pm. The ring has a circumference of 570 m, and is composed of 20 symmetrical cells. From experience on PLS-II (Shin et al., 2013 ), the length of the straight section is considered to be 6.5 m to accommodate two SCRF modules in one straight section. The PAL-4GSR lattice (Table 1, Fig. 1) contains a 2 T super-bend in the central dipole to produce radiation with a critical energy of 12 keV.

Table 1
Parameters relevant to the PAL-4GSR lattice

Parameter	Value	Unit
Energy	3	GeV
Emittance (flat / round)	90 / 58	pm
Circumference	569.96	m
Tune (x / y)	47.545 / 18.203	–
Natural chromaticity (x / y)	−96.0 / −57.9	–
Radiation loss per turn	0.468 (without insertion device)	MeV
Momentum compaction	1.45 × 10⁻⁴
Damping partition (H / V / L)	1.82 / 1.0 / 1.18
Damping time (H / V / L)	13.37 / 24.35 / 20.66	ms
Main RF voltage	2.15	MV

Figure 1
Twiss functions of PAL-4GSR (two cells) and the position of the transverse deflecting cavity and watching point.

The concepts of the ESRF-EBS and APS-U lattices were adopted in the PAL-4GSR lattice. The dispersion was deliberately enlarged between the first and second dipoles and between the sixth and seventh dipoles, then three chromatic sextupoles were located in this dispersion bump region to reduce the strength required to control the chromaticity. The betatron phase advances between the two dispersion bumps were set to Δφ_x ≃ 3π in the horizontal plane and Δφ_y ≃ π in the vertical plane; as a result, nonchromatic effects of the sextupoles are canceled out naturally. To minimize natural emittance, five-step longitudinal gradient dipoles and reverse bending magnets were considered (Streun & Wrulich, 2015 ; Nagaoka & Wrulich, 2007 ; Delahaye & Potier, 1989 ; Streun, 2014 ).

We performed tracking simulation to examine the resolution of the measurement using a transverse deflecting cavity (TDC) on PAL-4GSR. For tracking simulation, we used elegant software (Borland, 2000 ). A total of 100000 particles were generated at the position of the TDC (Fig. 1). They have a 58 pm (standard deviation) Gaussian distribution with matched Twiss functions in the horizontal and vertical planes, and ten lines of uniform density with maximum values of ±0.3% and ±24 mm in the longitudinal plane (Fig. 2). A watching point located at the left dispersion bump has a vertical phase advance of $[{\pi/2}]$ from the position of the TDC. For a TDC, we set a voltage of 4.5 MV and a frequency of 750 MHz, which yield ε = 0.02358. When the TDC was off, we observed five resolved distributions on the x axis at the watching point due to the correlation x₂ ≃ η₂δ₁ [Figs. 3(a) and 4(a)]. In the y axis, the distribution was not resolved [Figs. 3(a) and 4(b)]. Standard deviations of Gaussian peaks were 0.037 mm on the x axis and 0.022 mm on the y axis, which are explained by $[{\sigma}_{{x}_{2}}]$ ≃ $[{R}_{11}{\sigma}_{{x}_{1}}]$ + $[{R}_{12}{\sigma}_{{x}_{1}^{\,\prime}}]$ and $[{\sigma_{{y_2}}}]$ ≃ $[{R_{33}}{\sigma_{{y_1}}}]$ + $[{R_{34}}{\sigma}_{y_1^{\,\prime}}]$ . When the TDC was on, the x axis was not affected, but five resolved distributions appeared on the y axis [Fig. 3(b)]. The effective length on the y axis increased from 0.13 mm to 5.95 mm due to y₂ ≃ R₃₄εz₁ whereas the standard deviations of the Gaussian peaks did not change. These processes allow clear resolution of the five Gaussian peaks [Fig. 4(c)]. From the revealed Gaussian peaks with the use of a line distribution on the longitudinal plane, we define the intrinsic resolution on an axis as R_I = (distance between adjacent Gaussian peak) / (standard deviation of a Gaussian peak). R_I increases with increase in the clarity of distinction of the Gaussian peak on an axis. PAL-4GSR has R_I = 6.69 on the x axis and R_I = 64.68 on the y axis. The dispersion bump (for δ–x correlation) increases and the voltage of the TDC increases (for z–y correlation), so the resolution can be increased. Adjustment of dispersion bumps is constrained by lattice requirements, but the voltage of the TDC can be increased further without affecting lattice requirements and we can expect much better resolution than is currently achieved.

Figure 2
Longitudinal profiles of 100000 particles at the position of the crab cavity for examination of intrinsic resolution. Particles are distributed with a delta function in longitudinal phase space.

Figure 3
Beam distribution at the watching point with 100000 particles prepared for examination of intrinsic resolution. (a) TDC off; (b) TDC on.

Figure 4
Density distribution on the x and y axis for the beam distribution shown in Fig. 3

. (a) Density on the x axis when the TDC is on or off, (b) density on the y axis when the TDC is off, and (c) density on the y axis when the TDC is on.

4. Application on PAL-4GSR

A Gaussian bunch of 100000 particles in an equilibrium state was generated for the six-dimensional phase space with the round-beam mode. It had 58 pm emittance in both horizontal and vertical phase spaces. It should be mentioned that, for simplicity, distributed coupling errors are considered along the ring except for the region from the TDC and watching point to generate round beam. With a main RF voltage of 2.15 MV, its longitudinal distribution had σ_δ = 0.00108 and σ_z = 7.677 mm (Table 2). For a TDC, a voltage of 4.5 MV and a frequency of 750 MHz were also used.

Table 2
Particle distribution at the equilibrium

Parameter	Value	Unit
Horizontal emittance	58	pm
Vertical emittance	58	pm
Energy spread (r.m.s.)	0.00108	–
Bunch length (r.m.s.)	7.677	mm

4.1. Longitudinal emittance measurement

The longitudinal emittance can be written with the standard deviation as

$[{\varepsilon}_{z} = {\sigma}_{z}\,{\sigma}_{\delta}. \eqno(5)]$

Here, using equation (4), the standard deviations σ_z and $[{\sigma_\delta}]$ can be approximately converted to

$[{\sigma_x} \simeq {\eta_2}\,{\sigma_\delta} \eqno(6)]$

and

$[{\sigma}_{y} \simeq {R}_{34}\,\epsilon{\sigma}_{z}, \eqno(7)]$

respectively. Therefore, measurements of σ_x and σ_y directly lead to estimates of longitudinal emittance. The generated Gaussian bunch is deflected at the TDC. After a $[{\pi/2}]$ phase advance (at a watching point), the bunch's projection on the x–y plane has a clear Gaussian distribution [Fig. 5(b)], with σ_x = 0.197 mm and σ_y = 0.922 mm. From these values, re-projection using equation (4) gives σ_δ = 1.096 × 10⁻³ and σ_z = 7.680 mm, which have 1.46% and 0.04%, respectively, error relative to the original values. As a result, the longitudinal emittance from the measurement is calculated to be ɛ_z = 8.417 × 10⁻⁶ m, which is a 1.52% error relative to the original value. The original longitudinal profile at the TDC and the profile (Fig. 6) were obtained from re-projection using equation (4).

Figure 5
(a) x–y projection at the watching point and (b) longitudinal profile at the position of the crab cavity. No wakefield included.

Figure 6
Comparison of the original longitudinal profile at the crab cavity position (blue dots) and re-projection from equation (5)

(red dots). No wakefield included.

4.2. Measurement of the longitudinal phase space profile with instability

Beam manipulation in the longitudinal phase can be used to generate coherent radiation (Ratner & Chao, 2010 ) and beam dynamics in the longitudinal phase space to enable exploration of a new injection scheme (Kim et al., 2019; Aiba et al., 2015 ; Jiang et al., 2016 ; Jiang & Xu, 2018 ; Kuske et al., 2020 ). These goals invoke a need to measure the longitudinal beam profile. To generate a special shape in the longitudinal phase space, instabilities were deliberately induced by using wakefield data – here the impedance data of APS (Chae, 2003 , 2007 ; Lindberg & Blednykh, 2015 ). However, PAL-4GSR and APS have different characteristics such as circumference (PAL-4GSR: 570 m; APS: 1100 m), nominal energy (PAL-4GSR: 3 GeV; APS: 7 GeV), so use of these data can invoke instabilities in PAL-4GSR. We first estimated the current threshold I_threshold of the strong instability by following Boussard's criterion (Boussard, 1975 ),

$[{I_{\rm{threshold}}} = (2\pi)^{3/2} \, {{ \alpha_{\rm{c}}\sigma_{z}E\sigma_\delta^2 }\over{ cT_0\left|Z_\parallel/n\right| }}, \eqno(8)]$

where α_c is the momentum compaction, σ_z is the equilibrium bunch length, $[{\sigma_\delta }]$ is the equilibrium relative energy spread, c is the speed of light, T₀ is the revolution time, and $[\left|{{{{Z_\parallel}}/n}}\right|]$ is the effective longitudinal impedance. This conservative estimate gives I_threshold ≃ 0.37 mA; therefore we used a single bunch current of 7.7 mA (or single bunch charge of 15 nC) which is sufficiently high above the estimated threshold. Including the impedance data, a tracking simulation was conducted using a Gaussian bunch of 100000 particles in the equilibrium state. Oscillations of r.m.s. bunch length and r.m.s. energy spread along a number of turns show that both quantities increased rapidly after tracking started, reached their maximum within 2000 turns and eventually converged to a new equilibrium at ∼10000 turns (Fig. 7). The new equilibrium with the impedance data has 1.3 times larger bunch length and 1.8 times larger energy spread, compared with the original equilibrium. Those results imply that strong instability was driven well.

Figure 7
Oscillation of (a) r.m.s. bunch length and (b) r.m.s. energy spread versus turns when impedance data are included.

We next examined longitudinal beam profiles at 10000 turns (Fig. 8). After the kick of the TDC was applied, the longitudinal phase space was projected to the x–y plane. The central beam distribution split up and the outer beam distribution seems to have a spiral shape. Also, the center of the bunch was moved to ∼0.3 mm on the x axis. The overlap of the original longitudinal profile [Fig. 8(a)] and re-projection from the x–y plane [Fig. 8(b)] using equation (4) agreed well (Fig. 9).

Figure 8
Longitudinal profiles at (a) the position of the crab cavity, and (b) the x–y projection at the watching point. Wakefield is included.

Figure 9
Comparison of the original longitudinal profile at the crab cavity position (blue dots) and re-projection of the x–y profile at the monitor position using equation (4)

(red dots). Wakefield is included for a single bunch of 15 nC.

5. Conclusion

We have described a novel scheme to measure the emittance and phase space profile in the longitudinal plane by using correlations between time and the vertical coordinate, and between energy and the horizontal coordinate. A large dispersion bump has a strong correlation with energy and the horizontal coordinate, and the crab cavity has a strong correlation with time and the vertical coordinate. As a result, longitudinal emittance was estimated with <1.52% error in the PAL-4GSR lattice and micro-bunching instability was observed at the synchrotron radiation source point. This longitudinal profile measurement scheme will help to guide the manipulation of beams in longitudinal phase space.

APPENDIX A

Definitions of each matrix element of equation (2)

$[{R_{11}} = \left({{{{\beta _{x2}}} \over {{\beta _{x1}}}}} \right)^{1/2} \left({ \cos {\psi _x} + {\alpha _{x1}} \sin {\psi _x}} \right),]$

$[{R_{12}} = \left({{\beta }_{x1}{\beta }_{x2}} \right)^{1/2} \sin{\psi }_{x},]$

$[{R_{21}} = - {1 \over {\left({{\beta _{x1}}{\beta _{x2}}} \right)^{1/2} }}\big[{\left({1 + {\alpha _{x1}}{\alpha _{x2}}} \right) \sin {\psi _x} - \left({{\alpha _{x1}} - {\alpha _{x2}}} \right) \cos {\psi _x}} \big],]$

$[{R_{22}} = \left({{{{\beta _{x1}}} \over {{\beta _{x2}}}}} \right)^{1/2} \left({ \cos {\psi _x} - {\alpha _{x2}} \sin {\psi _x}} \right),]$

$[{R_{33}} = \left({{{{\beta _{y2}}} \over {{\beta _{y1}}}}} \right)^{1/2} \left({ \cos {\psi _y} - {\alpha _{y1}} \sin {\psi _y}} \right),]$

$[{R_{34}} = \left({{\beta }_{y1}{\beta }_{y2}} \right)^{1/2} \sin{\psi }_{y},]$

$[{R_{43}} = - {1 \over {\left({{\beta _{y1}}{\beta _{y2}}} \right)^{1/2} }}\left [{\left({1 + {\alpha _{y1}}{\alpha _{y2}}} \right) \sin {\psi _y} - \left({{\alpha _{y1}} - {\alpha _{y2}}} \right) \cos {\psi _y}} \right],]$

$[{R_{44}} = \left({{{{\beta _{y1}}} \over {{\beta _{y2}}}}} \right)^{1/2} \left({ \cos {\psi _y} - {\alpha _{y2}} \sin {\psi _y}} \right),]$

$[A = {R}_{21}{\eta }_{2}-{R_{11}}\eta_1^{\,\prime} + \eta_1^{\,\prime},]$

$[B = - {R_{12}}\eta_2^{\prime} + {R_{22}}{\eta _2} - {\eta _1},]$

$[C = - \int \limits_{{s_1}}^{{s_2}} {{\eta \left(s \right)} \over {\rho \left(s \right)}} \,{\rm{d}}s.]$

α, β are typical beta functions, η, η′ are dispersion functions, with corresponding subscript. ψ_x and ψ_y are, respectively, the horizontal and vertical phase advances between positions 1 and 2.

Acknowledgements

We thank G.-R. Hahn and T. Ha (PAL) for providing helpful information and many useful discussions.

Funding information

Funding for this research was provided by: National Research Foundation of Korea (grant No. NRF-2019R1C1C1003412; grant No. NRF-2019R1A2C1004862).

References

Aiba, M., Böge, M., Marcellini, F., Saá Hernández, A. & Streun, A. (2015). Phys. Rev. ST Accel. Beams, 18, 020701. Web of Science CrossRef Google Scholar
Borland, M. (2000). Elegant: A flexible SDDS-compliant code for accelerator simulation, Report No. LS-287. Advanced Photon Source, Argonne, IL, USA. Google Scholar
Boussard, D. (1975). Technical Report LabII/RF/Int/75-2. CERN, Geneva, Switzerland. Google Scholar
Chae, Y. (2003). Proceedings of the 2003 Particle Accelerator Conference (PAC2003), 12–16 May 2003, Portland, OR, USA, p. 3017. Google Scholar
Chae, Y.-C. (2007). Proceedings of the 2007 Particle Accelerator Conference (PAC2007), 25–29 June 2007, Albuquerque, NM, USA, p. 4336. Google Scholar
Chao, A. (2002). Lecture notes on topics in accelerator physics. Technical Report SLAC-PUB-9574. SLAC National Accelerator Laboratory, Menlo Park, CA, USA. Google Scholar
Delahaye, J. P. & Potier, R. (1989). Proceedings of the 1989 Particle Accelerator Conference (PAC1989), 20–23 March 1989, Chicago, IL, USA, pp. 1611–1613. Google Scholar
Emma, P., Frisch, J. & Krejcik, P. (2000). A transverse RF deflecting structure for bunch length and phase space diagnostics. Technical Report LCLS-TN-00-12. SLAC National Accelerator Laboratory, Menlo Park, CA, USA. Google Scholar
Huang, X. (2016). Phys. Rev. Accel. Beams, 19, 024001. Web of Science CrossRef Google Scholar
Huang, X., Hettel, B., Rabedeau, T., Safranek, J., Sebek, J., Tian, K., Wootton, K. P. & Zholents, A. (2019). Phys. Rev. Accel. Beams, 22, 090703. Web of Science CrossRef Google Scholar
Jiang, B. C., Zhao, Z. T., Tian, S. Q., Zhang, M. Z. & Zhang, Q. L. (2016). Nucl. Instrum. Methods Phys. Res. A, 814, 1–5. Web of Science CrossRef CAS Google Scholar
Jiang, S. & Xu, G. (2018). Phys. Rev. ST Accel. Beams, 21, 110701. Web of Science CrossRef Google Scholar
Kim, J., Jang, G., Yoon, M., Oh, B., Lee, J., Ko, J., Parc, Y., Ha, T., Kim, D., Kim, S. & Shin, S. (2019). Phys. Rev. Accel. Beams, 22, 011601. Web of Science CrossRef Google Scholar
Kuske, P., Li, J. & Aiba, M. (2020). Phys. Rev. Accel. Beams, 23, 030701. Web of Science CrossRef Google Scholar
Lindberg, R. R. & Blednykh, A. (2015). Proceedings of the Sixth International Particle Accelerator Conference (IPAC2015), 3–8 May 2015, Richmond, VA, USA, pp. 1822–1824. TUPJE077. Google Scholar
Liu, L. N., Milas, A. H. C., Mukai, X. R., Resende, A. R. D. & Rodriguet Sa, F. H. (2013). Proceedings of the 4th International Particle Accelerator Conference (IPAC2013), 12–17 May 2013, Shanghai, China, pp. 1874–1876. TUPWO001. Google Scholar
Loew, G. A. & Altenmueller, O. H. (1965). Design and applications of RF deflecting structures at SLAC. SLAC Report PUB-135. SLAC National Accelerator Laboratory, CA, USA. Google Scholar
Nagaoka, R. & Wrulich, A. F. (2007). Nucl. Instrum. Methods Phys. Res. A, 575, 292–304. Web of Science CrossRef CAS Google Scholar
Ratner, D. F. & Chao, A. W. (2010). Phys. Rev. Lett. 105, 154801. Web of Science CrossRef PubMed Google Scholar
Shin, S., Kwon, S., Kim, D., Kim, D., Kim, M., Kim, S., Kim, S., Kim, J., Kim, C., Park, B., Park, S., Park, S., Park, E., Son, Y., Yoon, J., Lee, B., Lee, E., Lee, J., Lee, H., Joo, Y., Choi, J., Ha, T., Hwang, W., Hwang, I., Lee, J., Oh, B., Lee, C., Lee, H., Kim, J., Hwang, J. Y., Nam, S. H. & Cho, M. (2013). J. Instrum. 8, P01019. Google Scholar
Steier, C., Byrd, J. M., De Santis, S., Nishimura, H., Robin, D., Sannibale, F., Sun, C., Venturini, M. & Wan, W. (2016). Proceedings of the 7th International Particle Accelerator Conference (IPAC 2016), 8–13 May 2016, Busan, Korea, p. 2956. Google Scholar
Streun, A. (2014). Nucl. Instrum. Methods Phys. Res. A, 737, 148–154. Web of Science CrossRef CAS Google Scholar
Streun, A. (2017). Editor. SLS-2 Conceptual Design Report. Paul Scherrer Institut, Villigen, Switzerland. Google Scholar
Streun, A. & Wrulich, A. (2015). Nucl. Instrum. Methods Phys. Res. A, 770, 98–112. Web of Science CrossRef CAS Google Scholar
Xiang, D. & Ding, Y. (2010). Phys. Rev. ST Accel. Beams, 13, 094001. Web of Science CrossRef Google Scholar
Zholents, A. (2015). Nucl. Instrum. Methods Phys. Res. A, 798, 111–116. Web of Science CrossRef CAS Google Scholar

This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.

JOURNAL OF
SYNCHROTRON
RADIATION

ISSN: 1600-5775

Volume 29| Part 1| January 2022| Pages 111-117

https://doi.org/10.1107/S1600577521011127

Open

access

Format		BIBTeX
		EndNote
		RefMan
		Refer
		Medline
		CIF
		SGML
		Plain Text
		Text

Format		BIBTeX
		EndNote
		RefMan
		Refer
		Medline
		CIF
		SGML
		Plain Text
		Text

Search IUCr Journals		doi		Advanced search
Author		volume	page

research papers\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

Single-shot measurement of longitudinal phase space beam profile in an electron storage ring

1. Introduction

2. Coupling of the y–z plane

3. PAL-4GSR and the intrinsic resolution

4. Application on PAL-4GSR

4.1. Longitudinal emittance measurement

4.2. Measurement of the longitudinal phase space profile with instability

5. Conclusion

APPENDIX A

Definitions of each matrix element of equation (2)

Acknowledgements

Funding information

References

research papers