CN111817786B - Transient energy chirp reconstruction method for electron beam - Google Patents

Transient energy chirp reconstruction method for electron beam Download PDF

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CN111817786B
CN111817786B CN202010564603.XA CN202010564603A CN111817786B CN 111817786 B CN111817786 B CN 111817786B CN 202010564603 A CN202010564603 A CN 202010564603A CN 111817786 B CN111817786 B CN 111817786B
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chirp
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张志钧
周诗怡
刘建胜
余昌海
秦志勇
王健硕
焦旭辉
严春晖
曹玉腾
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Shanghai Normal University
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    • H—ELECTRICITY
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    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
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    • H04B10/25137—Arrangements specific to fibre transmission for the reduction or elimination of distortion or dispersion due to chromatic dispersion using pulse shaping at the transmitter, e.g. pre-chirping or dispersion supported transmission [DST]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract

The invention discloses an electron beam transient energy chirp reconstruction method, and relates to the technical field of electron beam transient energy chirp diagnosis. The method for reconstructing the chirp of the transient energy of the electron beam adopts tightly focused chirped pulse laser a, interacts with a chirped electron beam b after being focused by a delayer (1) and a parabolic mirror (2), distributes the energy spectrum and the transverse divergence angle of the chirped electron beam b by an electron energy spectrometer (3), and applies Fourier transform of an energy domain to realize reconstruction of the chirp of the transient energy of the electron beam, and comprises the following steps: A-E. Compared with the prior art, the invention has the advantages that: first, the electron beam bunch transient energy chirp can be reconstructed. Secondly, the device is simple. The method can be realized only by depending on common mature, stable and reliable devices such as a paraboloidal mirror, an electronic energy spectrometer and the like. Thirdly, the expansibility is good. The adopted pulse laser can be expanded to any wave band. The method has great significance for the control optimization of the small accelerator and the dynamic behavior exploration and optimization of the electron beam in various novel accelerators.

Description

Transient energy chirp reconstruction method for electron beam
Technical Field
The invention relates to the technical field of electron beam transient energy chirp diagnosis, in particular to an electron beam transient energy chirp reconstruction method.
Background
In optics, the characteristic that the frequency of a signal varies with time is called chirp, which for a particle beam manifests as a change in the energy of the beam with time. The traditional femtosecond ultra-short electron beam energy chirp diagnosis method mainly adopts a radio frequency transverse deflector, such as an X-band. The main principle of the X-band is that when the electron beam is transmitted in the radio frequency cavity, a high-frequency radio frequency field is loaded in the transverse direction of the electron beam, and the radio frequency field has a certain gradient in the longitudinal direction, so that the electron beam generates transverse deflection depending on the longitudinal dimension, and the energy chirp diagnosis of the electron beam can be obtained by combining an electron energy spectrometer. In 2014, the U.S. Stanford linac center achieved diagnosis of energy chirp of electron beams with energy of 4.7GeV and 15.2GeV, pulse width of 2.6-11.3fs by using a 1m long X-band device [ V.A. Dolgashev et al, PhysRevsAB.17102801 (2014) ].
The radio frequency transverse deflector needs longer interaction time to ensure that the electron beam obtains enough transverse momentum due to the limitation of the field intensity of the radio frequency field, and the energy chirp distribution of the electron beam does not change in the process, namely the average energy of the electron beam is larger and generally in GeV magnitude, so that the transient energy chirp distribution of the electron beam is not obtained by the diagnosis in the mode. For low energy ultra short electron beams, the rf lateral deflector is not suitable because the chirp profile of the electron beam varies greatly over a short distance. The diagnosis of the transient energy chirp of the low-energy ultrashort electron beam is very critical to the generation and control of the high-quality and high-brightness electron beam in the accelerator, and particularly for the dynamic behavior exploration and optimization of the electron beam in various novel accelerators, the reconstruction of the transient energy chirp of the electron beam is a necessary condition for the complete phase space distribution description of the electron beam. Therefore, it is imperative to develop a new method for diagnosing the transient energy chirp of the electron beam.
Disclosure of Invention
The invention aims to overcome the defects and shortcomings in the prior art and provides an electron beam transient energy chirp reconstruction method.
Basic idea of the invention
The method comprises the steps of adopting tightly focused chirped pulse laser and a chirped electron beam to interact, and utilizing Fourier transform of an energy domain to realize reconstruction of electron beam transient energy chirp.
Brief description of the invention
The electromagnetic field component of an x-polarized, tightly focused chirped pulse laser can be expressed as follows:
Figure GDA0003012138800000021
Figure GDA0003012138800000022
Figure GDA0003012138800000023
Bx＝0， (4)
Figure GDA0003012138800000024
Figure GDA0003012138800000025
where xi is x/w0，υ＝y/w0，ε＝w0/zr，ρ2＝ξ2+υ2，f＝i/(z/zr+i)，
Figure GDA0003012138800000028
Is the Rayleigh length, w0Is a laser lumbar spot, and is characterized in that,
Figure GDA0003012138800000026
ω(ζ)＝1+b0zeta is the laser frequency of the linear chirp, zeta-z-t is the lag time, b0Is the laser frequency chirp coefficient, tau is the laser pulse width,
Figure GDA0003012138800000027
is a constant phase.
The invention adopts a normalized unit system: frequency vs laser center frequency omega0Normalized, length to laser center wavelength λ0Normalized, time-to-2 pi/omega0Normalization, velocity vs. vacuum light velocity c normalization momentum vs. mec normalization, field to mecω0a0And e, normalizing. m iseFor electron mass, e is the basic charge, a0Is normalized vector potential.
After the interaction process of the chirped pulse laser and the chirped electron beam is finished, the gain of the transverse momentum of the electron beam is delta px＝-e∫(Ex-By) dt. As shown in fig. 3, x-y-0 (E) is located on the axisx-By) Evolution over time and Δ p obtained after interaction under different conditionsxAnd (4) distribution. As can be seen from FIG. 3, the value of tan θ ═ w0/zrIn this case, the electron beam can obtain the maximum lateral momentum gain. And the chirped pulse laser is tightly focused, so that the interaction process is limited to an extremely short range, namely w0＝λ 01 μm as an example, 10zrAt 31.4 μm, the interaction process can be considered transient compared to the evolution time of the electron beam energy chirp. Introduction of alpha ═ px/pzThen alpha (p) can be obtained by an electron beam spectrometerz) Whereas α (ζ) can be obtained from the chirp of the chirped laser and α (p) is distributed by the diagonal distributionz) And α (ζ) to obtain pzAnd ζ, the energy chirp distribution of the electron beam can be obtained.
The linearly chirped electron beam case, in this case pz(ζ)＝C0+C1ζ. First, for C1I.e. whether the electron beam is positively or negatively chirped, alpha (p) which can be directly diagnosed by the electron beam spectrometer 3z) Judging that: to pairIn a positively chirped pulsed laser (b)0< 0), if α (p)z) The modulation period at high energy is greater than the modulation period at low energy, the electron beam is negatively chirped, i.e., C1Greater than 0, otherwise C1Is less than 0. On the other hand, for C1The specific numerical value of (A) can be represented by a (p)z) Is determined for alpha (p)z) By performing fourier transform based on energy domain, we can obtain:
Figure GDA0003012138800000031
wherein
Figure GDA0003012138800000032
For Fourier transform of alpha (zeta) in space domain, there are
Figure GDA0003012138800000033
Thus F2(ω)＝F0(ω). Two inferences can be drawn from equation (7): first, C1Will result in F1(omega) bandwidth change and frequency shift compared to F0(ω) spectral distribution, F1(ω) the bandwidth will shrink or broaden | C1I times, and the center frequency becomes ω0/|C1L, thus | C1L can be formed by F1(omega) in comparison with F0(ω) is obtained by a variation; second, C0To F1(ω) has no influence, C0Influencing only alpha (p)z) Distribution in the spatial domain, therefore C0Can be obtained directly from the energy spectrum of the electron beam. Taking FIG. 4 as an example, Δ W0/ΔW1≈5.3，ω0/ω14.9, and | C 15, satisfy | C1|≈ΔW0/ΔW1≈ω0/ω1And b < 0 and alpha (p)z) Modulation period is larger at low energy and C is obtained1Less than 0, plus
Figure GDA0003012138800000034
Thus obtaining C1≈-5，C0≈100。
Technical scheme of the invention
An electron beam transient energy chirp diagnosis reconstruction method comprises the following steps:
firstly, using FROG or SPIDER to measure the spectral phase and spectral intensity distribution of the chirped pulse laser to obtain the central frequency omega of the chirped pulse laser0And chirp parameter b0；
Establishing a diagnosis light path: the chirped pulse laser is focused by the joint delayer and the paraboloidal mirror and then interacts with the chirped electron beam, and then the chirped electron beam which is transversely modulated is freely transmitted into the electron spectrometer;
third, transverse modulation diagnosis: the time delay between the chirp pulse laser and the chirp electron beam is changed by adjusting the delayer, the position of the delayer corresponding to the occurrence and the end of the transverse modulation of the electron beam on the electronic energy spectrometer is recorded, a middle value is taken for experiment, and the transverse modulation alpha (p) of the chirp electron beam at the moment is obtained by the electronic energy spectrometerz) And its energy spectrum pz；
Fourthly, to alpha (p)z) Performing energy domain Fourier transform to obtain F1(ω) to give F1(ω) center frequency ω1And obtaining the mean value of the electron beam energy
Figure GDA0003012138800000041
The first-order energy chirp coefficient C of the chirped electron beam can be obtained by the following formula1Absolute value of (C) and constant term C0；
Figure GDA0003012138800000042
Combining chirp parameter b of chirp pulse laser0And alpha (p)z) To judge C1For b0< 0 if α (p)z) The modulation period at high energy is greater than the modulation period at low energy, and the chirped electron beam (b) is negatively chirped, i.e., C1≈ω0/ω1Otherwise, C1≈-ω0/ω1。
As described above, the present invention provides a method for reconstructing electron beam transient energy chirp by using a tightly focused chirped pulse laser, which can effectively diagnose the transient energy chirp of a femtosecond level or even shorter low-energy electron beam, and can implement fast real-time reconstruction of the energy chirp distribution of the electron beam by using the fourier transform of an energy domain, which is very critical to the generation and control of a high-quality and high-brightness electron beam in an accelerator, and is especially significant to the exploration and optimization of the dynamic behavior of the electron beam in various novel accelerators.
Compared with the prior art
1. The electron beam transient energy chirp can be diagnosed. There are no other schemes currently available to enable the diagnosis of transient energy chirp of an electron beam.
2. The device is simple and convenient. The method can be realized only by depending on common mature, stable and reliable devices such as a paraboloidal mirror, an electronic energy spectrometer and the like without redesigning a complex device.
3. And the expansibility is good. The adopted pulse laser can be expanded to any wave band.
Drawings
FIG. 1 is a schematic diagram of an apparatus for electron beam transient energy chirp reconstruction according to the present invention;
FIG. 2 is a flow chart of an electron beam transient energy chirp reconstruction method according to the present invention
FIG. 3 embodiment: tan θ ═ w0/zrIn this case, the on-axis (x ═ y ═ 0) field (E)x-By) Distribution and lateral momentum gain deltap of electrons on the rear axis after interaction under different theta conditionsx；
FIG. 4 embodiment: alpha (zeta) and alpha (p) after the interaction between the tightly focused chirped pulse laser and the chirped electron beam is finishedz) Corresponds to F1(omega) and F0(ω) frequency domain spectral distribution plot.
Detailed Description
The invention is further described in the following with reference to examples and figures
The invention relates to a diagnosis device of an electron beam transient energy chirp reconstruction method (as shown in figure 1). The chirped pulse laser a is focused by the delayer 1 and the parabolic mirror 2 and then interacts with the chirped electron beam b, the energy spectrum and the transverse divergence angle distribution of the chirped electron beam b are diagnosed by the electron energy spectrometer 3, and the modulation is carried out to reconstruct the method (as shown in the attached figure 2), which comprises the following steps:
A. measuring the spectral phase and spectral intensity distribution of the chirped pulse laser a by FROG or SPIDER to obtain the center frequency omega of the chirped pulse laser a0And chirp parameter b0；
B. Establishing a diagnosis light path: the chirped pulse laser a is focused by the delayer 1 and the parabolic mirror 2 and then interacts with a chirped electron beam b, and then the chirped electron beam b which is transversely modulated is freely transmitted into an electron energy spectrometer 3;
C. in the transverse modulation diagnosis, the time delay between the chirped pulse laser a and the chirped electron beam b is adjusted and changed through the delayer 1, the position of the delayer 1 corresponding to the appearance and the end of transverse modulation of the electron beam b on an electron energy spectrometer 3 is recorded, an intermediate value is taken for experiment, and the transverse modulation alpha (p) of the chirped electron beam b at the moment is obtained through the electron energy spectrometer 3z) And its energy spectrum pz；
D. For alpha (p)z) Performing energy domain Fourier transform to obtain F1(ω) to give F1(ω) center frequency ω1And obtaining the b energy mean value of the chirped electron beam
Figure GDA0003012138800000061
And obtaining the first-order energy chirp coefficient C of the chirped electron beam b through the following formula1Absolute value of (C) and constant term C0；
Figure GDA0003012138800000062
E. Combining chirp parameters b of chirped pulse laser a0And alpha (p)z) To judge C1For b0< 0 if α (p)z) The modulation period at high energy is larger than that at low energy, the chirped electron beam b is negatively chirped, i.e. C1≈ω0/ω1Otherwise, C1≈-ω0/ω1。
Further, the delayer 1 is composed of four-side plane reflectors, the delayer 1 is controlled by the translation stage, and the delay control precision is 0.2 fs.
Further, the F-number of the paraboloidal mirror 2 is 2.
In summary, the present invention provides a method for reconstructing electron beam transient energy chirp by using a tightly focused chirped pulse laser, which can effectively diagnose femtosecond-level or even shorter transient energy chirp of low-energy electron beams, and can realize fast real-time reconstruction of the energy chirp distribution of the electron beams by using fourier transform of an energy domain. On the one hand, the method is very critical to the generation and control of high-quality and high-brightness electron beams in the accelerator, is suitable for complete phase space parameter diagnosis of the electron beams in the small accelerator, and provides an important technical scheme for important application of small radiation sources such as optimization and control of an X-ray source and the like; on the other hand, the invention has great significance for the exploration and optimization of the dynamic behavior of the electron beam in various novel accelerators, including a medium accelerator, a plasma accelerator and the like, in the research in the fields, how to control the energy chirp evolution of the electron beam is an important premise for obtaining the low-energy-dispersion high-quality electron beam, and is also an urgent problem to be solved whether a compact electron beam source and a radiation source can realize effective application, so that the realization of the transient energy chirp reconstruction of the electron beam has great promotion effect on the application research in the front-edge fields.

Claims (3)

1. A chirp pulse laser a interacts with a chirp electron beam b after being focused by a delayer (1) and a parabolic mirror (2), and diagnoses the energy spectrum and the transverse divergence angle distribution of the chirp electron beam b by an electron energy spectrometer (3), which is characterized by comprising the following steps:
A. measuring the spectral phase and spectral intensity distribution of the chirped pulse laser a by FROG or SPIDER to obtain the center frequency omega of the chirped pulse laser a0And chirp parameter b0；
B. Establishing a diagnosis light path: the chirped pulse laser a is focused by the delayer (1) and the parabolic mirror (2) and then interacts with the chirped electron beam b, and then the chirped electron beam b which is transversely modulated is freely transmitted into the electron energy spectrometer (3);
C. transverse modulation diagnosis: the time delay between the chirped pulse laser a and the chirped electron beam b is adjusted and changed through the delayer (1), the position of the delayer (1) corresponding to the appearance and the end of the transverse modulation of the electron beam on the electron energy spectrometer (3) is recorded, an intermediate value is taken for carrying out an experiment, and the transverse modulation alpha (p) of the chirped electron beam b at the moment is obtained through the electron energy spectrometer (3)z) And its energy spectrum pz；
D. For alpha (p)z) Performing energy domain Fourier transform to obtain F1(ω) to give F1(ω) center frequency ω1And obtaining the b energy mean value of the chirped electron beam
Figure FDA0003012138790000011
And obtaining the first-order energy chirp coefficient C of the chirped electron beam b through the following formula1Absolute value of (C) and constant term C0；
Figure FDA0003012138790000012
E. Combining chirp parameters b of chirped pulse laser a0And alpha (p)z) Distribution characteristic judgment of C1For b0< 0 if α (p)z) The modulation period at high energy is larger than that at low energy, the chirped electron beam b is negatively chirped, i.e. C1≈ω0/ω1Otherwise, C1≈-ω0/ω1。
2. The electron beam transient energy chirp reconstruction method according to claim 1, wherein the retarder (1) is composed of four plane mirrors, the retarder (1) is controlled by a translation stage, and the delay control precision is 0.2 fs.
3. The electron beam transient energy chirp reconstruction method according to claim 1, wherein the F-number of the parabolic mirror (2) is 2.
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