Study of beam transverse properties of a thermionic electron gun for application to a compact THz free electron laser Tongning Hu, Yuanji Pei, Bin Qin, Ping Tan, Qushan Chen, Lei Yang, and Ji Li Citation: Review of Scientific Instruments 85, 103302 (2014); doi: 10.1063/1.4897481 View online: http://dx.doi.org/10.1063/1.4897481 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Generation of a 500-keV electron beam from a high voltage photoemission gun Appl. Phys. Lett. 102, 234103 (2013); 10.1063/1.4811158 Full scale simulation of a field-emitter arrays based electron source for free-electron lasers J. Vac. Sci. Technol. B 24, 892 (2006); 10.1116/1.2181988 Basic R&D Studies for Lower Emittance Polarized Electron Guns AIP Conf. Proc. 675, 1068 (2003); 10.1063/1.1607298 Free-electron maser driven by a two-stage ferroelectric electron gun J. Appl. Phys. 93, 2304 (2003); 10.1063/1.1539540 Radio-frequency photocathode guns triggered by free electron laser light J. Appl. Phys. 93, 641 (2003); 10.1063/1.1525859
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 103302 (2014)
Study of beam transverse properties of a thermionic electron gun for application to a compact THz free electron laser Tongning Hu,1,a) Yuanji Pei,2,a) Bin Qin,1 Ping Tan,1 Qushan Chen,1 Lei Yang,1 and Ji Li2 1 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074, China 2 National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, China
(Received 9 December 2013; accepted 27 September 2014; published online 13 October 2014) A novel thermionic electron gun adopted for use in a high power THz free electron laser (FEL) is proposed in this paper. By optimization of the structural and radiofrequency (RF) parameters, the physical design of the gun is performed using dynamic calculations. Velocity bunching is used to minimize the bunch’s energy spread, and the dynamic calculation results indicate that high quality beams can be provided. The transverse properties of the beams generated by the gun are also analyzed. The novel RF focusing effects of the resonance cavity are investigated precisely and are used to establish emittance compensation, which enables the injector length to be reduced. In addition, the causes of the extrema of the beam radius and the normalized transverse emittance are analyzed and interpreted, respectively, and slice simulations are performed to illustrate how the RF focusing varies along the bunch length and to determine the effects of that variation on the emittance compensation. Finally, by observation of the variations of the beam properties in the drift tube behind the electron gun, prospective assembly scenarios for the complete THz-FEL injector are discussed, and a joint-debugging process for the injector is implemented. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4897481] I. INTRODUCTION
Among the diverse range of available terahertz (THz) sources, free electron lasers (FELs) have been the focus of recent research interest because of their distinct merits, such as high power and continuously tunable radiation.1, 2 For commercial and civil use, apart from high average power requirements, low costs and compact structures must also be considered. Cost-effective FELs with linear accelerator injectors have the potential to achieve a balance among these conditions.3 With its high stability and long lifetime, the conventional injector system using a thermionic cathode followed by a buncher system has been applied widely.4–6 With the benefits of many modifications and upgrades, the thermionic injector used in the SPring-8 Angstrom Compact Free Electron Laser (SACLA)7 has achieved improved beam performance: the emittance value is maintained at around 1π mm · mrad, and the resulting beam charge increased up to 250 pC.8 However, the subharmonic buncher and the long drift section contained therein preclude reduction of the device size, which is essential for widespread distribution of THz sources. Also, recent research indicates that a thermionic electron gun with two independent tunable cavities (ITCs)9 can produce a more compact injector layout by using velocity bunching to minimize the energy spread.10, 11 In addition, the back bombardment effect is eliminated almost completely by implementation of an external cathode (EC),12, 13 and the insufficient a) Authors to whom correspondence should be addressed. Electronic ad-
dresses: [email protected] and [email protected]
0034-6748/2014/85(10)/103302/8/$30.00
charge bottleneck can also be overcome by optimizing the dimensions and the RF parameters of the ITC cavities.14 After careful consideration, the EC-ITC radiofrequency (RF) gun has been adopted for use in the THz-FEL oscillator proposed by Huazhong University of Science and Technology (HUST) in combination with University of Science and Technology of China (USTC),15 which aims to generate 50 – 100 μm coherent radiation with 1 MW-level peak power on a table-top scale. In the conceptual design, the injector mainly consists of the EC-ITC gun and a booster linac coupled to focusing coils;16 the corresponding scheme for the injector is shown in Fig. 1. According to the formula used to define beam brightness,17 the transverse parameters of the bunch, such as the beam radii and the transverse emittance, must be confined within an acceptable scale. Previous research on the standing-wave cavity has shown that the RF focusing of the cavity itself seems to serve the purpose of beam cross-section compression,18 and that the RF focusing can be enhanced by a higher accelerating gradient, which is usually limited by the power of the available RF sources and the breakdown field strengths of the cavities. Sun et al.19 proposed an approach using asymmetric RF fields to enhance the RF focusing and RF phase focusing (transverse RF focusing that depends on the beam phase); this approach has been validated by the latest beam dynamics,20 and the results agree effectively with test results. Another intrinsic drawback of the thermionic electron gun is its considerable transverse emittance, which conflicts with the requirements of the HUST THz-FEL. To a certain extent, the concepts of emittance growth and compensation of photocathode injectors are of sufficient significance to be used
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FIG. 1. Schematic view of the HUST THz-FEL injector.
for reference here, because of the in-depth studies that have been performed and the various solutions offered by these studies.21–24 Although the physical design of the enhanced EC-ITC RF gun has been performed and the simulation results fulfill the design targets, the elaborate transverse properties must still be investigated using slice simulations, and the effects of RF focusing on emittance compensation must also be explored more intensively. Additionally, further studies of the injector assembly scheme are still necessary, and will have a significant impact on the scale of the facility. This paper will address all the above subjects. II. PHYSICAL DESIGN OF THE EC-ITC RF GUN
As mentioned above, the intrinsic drawbacks of ordinary thermionic electron guns, and particularly the insufficient bunch charge, can be overcome using the EC-ITC RF gun. Based on multi-cavity RF gun theory, the four main design criteria of the EC-ITC RF gun are summarized as follows. (1) The drift tube length L between the two cells must be sufficient to attenuate the electric field strength EL , which is supposed to be 0.1% of the peak value E0 . The relational expressions are listed as follows: EL = e−αL , E0 2π α= λ
2.405λ 2π b
(1)
2 − 1,
(2)
where α is the attenuation constant, λ is the RF wavelength, and b is the drift tube radius. (2) Because the relative velocity of the synchronous electron β e < 1, the length Li of the ith cell of the ITC should be set appropriately in non-relativistic cases, λ Li = βpi , 2
FIG. 2. (a) Two-dimensional sketch of the ITC with field distributions and chamfer illustration, and (b) three-dimensional sketch of the ITC with couplers and plunger.
ments indicated that the ITC is not in danger of reaching its breakdown field strength.12 (4) Two input couplers are applied to supply power independently to the two cells of the ITC and are assembled vertically to avoid spatial conflicts. A plunger is inserted into Cell 1 for frequency tuning. A three-dimensional drawing of the ITC with the couplers and plunger is shown in Fig. 2(b). In the design of the HUST THz-FEL injector, a gridded electron gun with double anodes is adopted as the beam source and can produce a 5 A, 15 keV DC beam with 1 mm waist radius and a 42 mm shot range,14 and the subsequent ITC is implemented to extract a micro-bunch train with high brightness. By adjusting the cavity dimensions and the RF parameters in Superfish and Parmela simulations, the optimal output states of the EC-ITC RF gun are derived as shown in Fig. 3, while the specific bunch performance and RF parameters are listed in Table I. During the simulation, OPERA/CST is used to generate the beam distribution from the electron gun,14 and the peak electrical field strengths of the two cells are 40.45 MV/m and 89.28 MV/m. When output from Cell-1 of the EC-ITC RF gun, the beam kinetic energy obtained is 442 keV, the bunching process is almost complete and the micro-bunch head contains a charge of over 200 pC. This shows that the HUST THz-FEL injector, which has a more compact layout, can produce a performance similar to that of the SACLA injector. Additionally, because of the low energy spread of the ITC gun, the elongation of the bunch extracted from Cell-2 can be ignored within a short range, and the longitudinal properties will therefore not be concentrated thereafter. However, the transverse properties of Cell-2, such as the radius and the emittance, must be analyzed and discussed emphatically with regard to their contributions to the final beam brightness.
(3)
where β pi is the equivalent phase velocity of the ith cell, and obeys the identity β ei ≡ β pi . (3) To avoid cutting burrs during machining, simple external arcs are used rather than nose cones, and a 0.03 mm interspace is reserved for diamond tool return, as illustrated in Fig. 2(a). Additionally, artificial machine tools are adopted rather than numerically controlled machine tools, so that the effects of the machining accuracy can be reduced. Under these conditions, previous experi-
III. TRANSVERSE FOCUSING OF CELL-2 IN THE EC-ITC RF GUN
By consideration of the overall system requirements, the field configuration and the input beam parameters of the ECITC RF gun have already been determined. However, because of the defocusing forces that are induced by the RF fields and the space-charge field, the extracted high current and low energy beams are subjected to detrimental effects on their transverse beam sizes, and RF phase focusing has been
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FIG. 3. Output states of the EC-ITC RF gun: (a) Phase spectrum; (b) transverse spot; (c) longitudinal phase space; and (d) energy spectrum.
shown to have the potential for beam envelope refinement. Because Cell-2 can be regarded as a focusing lens, analysis of the equivalent focusing properties has significance for the assembly positions and the design targets of the downstream equipment. A. Focusing properties of super-short bunches
In the case of axisymmetric standing-wave cavities operating in the TM010 mode, only the radial force contributes to
Beam energy Micro-bunch head charge Micro-bunch length (FWHM), σ z Energy spread (FWHM) Normalized emmittance, n Micro-bunch radius (rms) Micro-bunch repetition rate Macro-pulse current Macro-pulse duration Macro-pulse repetition rate
where r is the radial position, and β is the electron speed as a proportion of the light speed c. The longitudinal electric field along the z axis can be expressed as Ez (z, t) = Ez (z) cos(kct + φ0 )
TABLE I. Main EC-ITC RF gun parameters. Parameter
the radial motion of the internal electrons. On the basis of the Maxwell equations, by taking only the first order of the transverse electromagnetic fields into account and by using the approximate condition z˙ = βc, the radial force can be written as ∂Ez (z, t) er ∂Ez (z, t) β − × , (4) Fr = − 2 ∂z c ∂t
Value 2.6 MeV 201 pC 1.5 ps 0.27% 6.5π mm · mrad 0.9 mm 2856 MHz 0.574 A 4-6 μs 10–200 Hz
= Em sin
kz cos(kct + φ0 ). βp
(5)
Here, t is the electron injection time related to the synchronous electron, φ 0 is the synchronous electron phase, and Em is the axial electrical field amplitude. We assume that the injected bunch has an infinitesimal length and that its radius is sufficiently small such that the transverse component of the energy spread can be neglected. Additionally, the bunch is always on the crest of the RF field, which means that the bunch with the centered synchronous electron can be called the synchronous slice. Meanwhile, the slices located in front of and behind the RF crest can be
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By substituting Eq. (6) into Eq. (4), and using k = 2π /λ and β p = 2L/λ, a simplified expression for Fr can be written as π π erEm cos z . (7) Fr = − 2L L Based on Eq. (7), the radial motions of the synchronous slice are determined as follows: (1) In the first part of the cavity, z ∈ [0, L/2], Fr < 0, and thus the synchronous slice is subjected to a focusing effect. (2) In the second part of the cavity, z ∈ [L/2, L], Fr > 0, and thus the synchronous slice is subjected to a defocusing effect. (3) Fr is proportional to Em . To provide intuitive demonstrations of the focusing properties of Cell-2, a simulated cylindrical bunch with a uniform density distribution and a super-short length is used as the input to Cell-2. By selecting the same peak electric field strength value as that mentioned in Sec. II, and by tuning the RF field phase to ensure that the input bunch will be on the crest of the accelerating electrical field, the variations in the transverse size σ x along the z axis under different field strengths have been plotted in Fig. 4, where the starting position is the entrance to Cell-2. Obviously, after entering the main cavity (z = 1.8 cm ∼ 4.524 cm) of Cell-2, the super-short bunch is subjected to a strong focusing effect in the first half of the cavity and a weak defocusing effect in the second half of the cavity. Because the former effect is dominant, the focusing trend only slows in the second half of the cavity, and the beam output from Cell-2 (z = 6.5 cm) continues focusing until it reaches the focal point in the later drift tube. Additionally, the focusing effect becomes stronger under higher electric 2.5
67.0MV/m, without space−charge 89.3MV/m, without space−charge 111.9MV/m, without space−charge 67.0MV/m, with space−charge 89.3MV/m, with space−charge 111.9MV/m, with space−charge
σx (mm)
2 1.5
0.5 5
10 z(cm)
15
(a)
15
20
FIG. 4. σ x variations along the z axis with different peak electric field values.
without space−charge with space−charge
10 5 0
70
80
90
100 110 Em (MV/m)
120
130
140
0.2 without space−charge with space−charge (b)
0.15 0.1 0.05 0
70
80
90
100 110 Em (MV/m)
120
130
140
FIG. 5. (a) Focusing length variations and (b) focal radius variations of Cell-2 of the EC-ITC RF gun.
fields, which is in turn evidence for the third conclusion drawn from Eq. (7). In addition, Fig. 5 shows how Em affects the focal length and the focal radius, while the space-charge field plays a subdued role for both of these parameters. However, the effects of the space-charge field will saturate when Em > 140 MV/m, as shown in Fig. 5, because the electron beams approach the speed of light. B. Focusing properties of bunches with finite lengths
In the qualitative analysis of the radial motion and beam dynamics of the synchronous slice in Subsection III A above, several approximate conditions are applied and the conclusion of the general focusing trend of the super-short bunches at the optimal acceleration phases is derived. However, in view of the actual situation of bunches with finite lengths, the internal slices at different longitudinal positions are subjected to the different radial forces induced by the RF phase differences that they encounter, meaning that the time dependence of the RF fields must be taken into account. Using the differ∂Ez (z,t) ∂E (z,t) dz + z∂t dt, Eq. (4) can ential operator dEz (z, t) = ∂z be transformed into Fr = −
1
0 0
20
Focal length (cm)
defined as advancing slices and lagging slices, respectively. The synchronous slice always matches the axial electrical field amplitude in the accelerating cavity, which means that the time dependence of the RF fields can be neglected, and Eq. (5) can be simplified as Ez (z, t) = Em sin (kz/β p ). Therefore, the approximate conditions can be obtained as follows: ⎧ ∂Ez (z, t) ⎪ ⎪ =0 ⎨ ∂t (6) π ⎪ ∂Ez (z, t) π Em ⎪ ⎩ = cos z . ∂z L L
Focal radius (mm)
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er dEz (z, φ) ker ∂Ez (z, φ) + , 2 dz 2βγ 2 ∂φ
(8)
where γ is the relativistic factor, and Ez (z, t) is replaced by Ez (z, φ) by using φ = kct + φ 0 , where φ is the electron phase related to the synchronous electron. The first term on the right-hand side of Eq. (8), FI dE (z,φ) = − er2 zdz is the total derivative of the longitudinal electric fields along the electron trajectory, which act as an electrostatic lens.18 The second term, FII , determines the RF phase focusing force,19 which will be the focus of study here and
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can be expressed as
with constant energy in free space, it is more convenient to replace the physical phase space with a geometric phase space; meanwhile, the rotation between the horizontal and vertical phase spaces of the axially symmetrical bunches are very much alike, and thus the normalized transverse emittance can be defined by Eq. (10):
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FI I = =
ker ∂Ez (z, φ) 2βγ 2 ∂φ ker πz cos φ. sin 2 2βγ L
(9)
Because sin πz consistently remains positive in the cavL ity, the sign of FII depends on cos φ. The function of FII on the beam radial motion can be concluded as follows: (1) In the case of advancing slices, φ ∈ (0, π /2), FII > 0 and acts as a defocusing force. (2) In the case of lagging slices, φ ∈ (π /2, π ), FII < 0 and acts as a focusing force. (3) FII does not affect the synchronous slice (φ = π /2), which is time-independent. To inspect the focusing effect, including RF phase focusing in Cell-2, an initial 200 pC, 442 keV beam with width of 40◦ is launched in Parmela; the beam has the same shape and distributions as the ultra-short bunch described in Subsection III A. The theoretical derivation is confirmed by the beam dynamic results shown in Fig. 6(a), while Fig. 6(b) indicates that the advancing beams are bunched while lagging beams are debunched. Although stronger transverse focusing can be obtained by placing more electrons behind the RF crest, the bunch elongation cannot be ignored for the HUST THz-FEL injector. IV. EMITTANCE COMPENSATION
The beam emittance is the region in phase-space that is occupied by the particles in a beam.25 For electrons
n,x =
N
xi2
i=1
N
xi2 −
N
i=1
2 xi xi
.
(10)
i=1
According to previous researchers, the transverse emittance can be simply classified into two typical types, the projected emittance and the slice emittance, and the former is conventionally discussed in emittance compensation. Several approaches have been suggested for emittance minimization, including use of a solenoid magnet, RF radial focusing, use of alternative cathode materials and design of a specific RF gun.24 While the concept of emittance compensation is generally discussed for photocathode guns for short-wavelength radiation applications, the issue of emittance growth has yet to be settled for high brightness injectors like the HUST THzFEL injector, and thus Hu et al.16 introduced a standard emittance compensation scenario using a short magnetic lens and focusing coils, which are inevitably accompanied by loss of system compactness. A. Beam emittance of the EC-ITC RF gun
To be as close to the real situation as possible, a cutoff head from the bunch extracted by the EC-ITC RF gun is used, which is the same condition as that of Sec. II. After drifting in free space, the transverse property variations of the bunch head are given in Fig. 7. 2.5
4 advancing bunch synchronous bunch lagging bunch
2
(a)
3.5
σx (mm)
σz (mm)
N βγ
with space−charge without space−charge (a)
1.5 1
3
0.5 2.5
2
4
6
8
10 12 z(cm)
14
16
18
0 0
20
with space−charge without space−charge
advancing bunch synchronous bunch lagging bunch
mrad)
(b)
2
n,x (mm
σx (mm)
40
60 z(cm)
80
100
120
80
100
120
8
3 2.5
20
1.5 1
7
(b)
6 5
0.5 0 0
5
10 z(cm)
15
20
FIG. 6. (a) σ x variations and (b) σ z variations along the z axis for the different phases.
4 0
20
40
60 z(cm)
FIG. 7. (a) Transverse size (rms) variations and (b) normalized transverse emittance (rms) variations of the EC-ITC RF gun along the z axis.
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FIG. 8. Longitudinal profiles [(a), (b), (c)] and transverse phase spaces [(d), (e), (f)] of the bunch head at the exit of the EC-ITC RF gun, the position of the first minimum of σ x and the position of the second minimum of σ x , respectively.
The beam envelope continues to decrease in free space until it is more than 40 cm away from the exit of Cell-2, as shown in Fig. 7(a); this is caused by the focusing effect of Cell-2. Observation of Fig. 7(b) indicates that, under space-charge effects, two minimal values for the normalized transverse emittance n, x are explored in free space. By borrowing the concept of emittance compensation from photocathode guns, the beam reconfigurations can be interpreted as follows: (1) The effect of the equivalent focusing lens of Cell-2 acts as a conventional approach for projected emittance compensation, and the first minimum of n, x is obtained near the focal point; the corresponding bunch profile and the transverse phase space are shown in Figs. 8(b) and 8(e), respectively. (2) Because of its internal particle distribution, the extracted bunch evolves through the spatial expansion of differing radii to achieve a quasi-ellipsoidal formation, which then has a linear space-charge field on all spatial coordinates.23 This is similar to the temporal shaping technique of driven laser pulses that is used in photocathode injectors. The bunch (x, z) distributions at various positions in the subsequent drift tube are clearly displayed in Figs. 8(a)–8(c). Here, the beam has 2.6 MeV mean energy, and its transverse dynamics are spacecharge dominated. An “inflated” ellipsoidal beam shape can clearly be seen in Fig. 8(c), which is obtained purely from space-charge effects. The second minimum of n, x is therefore obtained as shown in Fig. 7(b), while the corresponding transverse phase space is displayed in Fig. 8(f).
B. Slice simulations for the EC-ITC RF gun
To show how the RF focusing varies along the bunch length and the effect of that variation on emittance compensation, slice simulations must be implemented for Cell-2. In the simulation, the bunch extracted from Cell-1 is divided into several slices with widths of 1 ps in the longitudinal direction. Apparently, the transverse properties of the slices vary differently from each other along the z axis, as shown in Fig. 9. While the initial transverse properties of the slices are different to each other, it is clear that the focusing capability of a lagging slice is much stronger than that of an advancing slice, as shown in Fig. 9(b), which is similar to the result concluded in Subsection III B. Also, Fig. 9(a) shows that the emittance of the lagging slice changes more slowly than that of the advancing slice. Therefore, addition of more particles to the lagging phase helps to strengthen the effects of RF phase focusing of Cell-2 on emittance compensation. V. ASSEMBLY OUTLOOK
For the future assembly of the HUST THz-FEL, apart from the basic compactness requirement, several other aspects must be considered for the injector assembly scenario, which are described as follows: (1) Adequate space must be reserved for a toroid at a downstream location of the EC-ITC RF gun for beam testing. (2) The bunches generated by the EC-ITC RF gun must enter the booster linac as quickly as possible to guarantee that their properties will not degrade sharply. (2) To resolve the contradiction above, a drift tube must be used between the EC-ITC RF gun and the booster
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10
1.1
advancing slice synchronous slice 1st lagging slice 2nd lagging slice 3rd lagging slice
with space−charge without space−charge
1
(a) σz (mm)
n,x (mm mrad)
15
5
(a)
0.9 0.8 0.7
0 0
20
40
60 z(cm)
80
100
120
0.6 0
2.5
1.5
5
advancing slice synchronous slice 1st lagging slice 2nd lagging slice 3rd lagging slice
Energy spread(rms)
σx (mm)
2
(b)
1 0.5 0 0
20
40
60 z(cm)
20
40
−3
80
100
120
x 10
4
with space−charge without space−charge
60 z(cm)
80
100
120
80
100
120
(b)
3 2 1 0 0
20
40
60 z(cm)
FIG. 9. (a) n, x variations and (b) σ x variations of the different slices in the bunch extracted from the EC-ITC RF gun.
FIG. 10. (a) Longitudinal length (rms) variations and (b) energy spread (rms) variations of the EC-ITC RF gun along the z axis.
linac, while associated focusing magnets must be used simultaneously around the tube and the subsequent linac for radial compression and suppression of emittance growth. (3) To prevent the deflection effects of the magnetic fields acting on low-energy electrons, the focusing coils must be located away from both the cathode and Cell-1.
Depending on the beam dynamics in the EC-ITC RF gun and the subsequent drift tube, the first minimum of n, x is clearly located at a position 34 cm away from the exit of the gun, and the minimum of σ x appears later, 46 cm away from the exit of the gun, as shown in Fig. 7. Additionally, the variations of both the bunch length and the energy spread are shown in Fig. 10, which indicates that both of the longitudinal properties only degrade slightly up to 25 cm away from
FIG. 11. Beam property variations along the beamline after the EC-ITC RF gun: (a) transverse size, (b) normalized transverse emittance, (c) energy spread, and (d) bunch length.
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the exit of the gun, but deteriorate rapidly later; a position near the transition point might therefore be suitable for the entrance to the linac. Based on numerous optimizations, the optimal assembly positions for the booster linac and the associated focusing coils are determined, and these positions are validated by start-to-end dynamic calculations. The property variations in the downstream drift tube and the linac are shown in Fig. 11, which indicates that the injector assembly scenario fulfills the compact structure and high performance requirements. While the short magnetic lens around the drift tube in the original focusing scheme16 can be avoided, adequate space is still reserved for this lens in case it is required for uncertain operations. VI. DISCUSSION AND CONCLUSIONS
The physical design of the EC-ITC RF gun to be used for the FEL injector is conducted using the PARMELA code, and the space-charge effects are calculated using the SCHEFF routine in PARMELA. According to the beam dynamics results, high quality bunches with effective charge of over 200 pC can be obtained using this type of injector. Compared with traditional thermionic guns, the EC-ITC RF gun adopted here can overcome notable problems, such as high energy spread and high transverse emittance, while having a compact and robust structure, unlike complex photocathode RF guns. In other words, the EC-ITC RF gun fulfills the requirements for use in the HUST THz-FEL. For confinement of the beam radius, the RF focusing and RF phase focusing of Cell-2 of the EC-ITC RF gun are carefully analyzed, and the cell dimensions are refined. In addition, the beam dynamics indicate that the space-chargedominated relativistic beam extracted by the EC-ITC RF gun is not subjected to transverse beam profile expansion before entering the linac. This means that Cell-2 plays a role in RF focusing, which can then release the space occupied by the magnetic lens in the original assembly scenario. In addition, by borrowing the conceptual framework from previous works in the context of emittance growth and compensation in photocathode guns, the variations in the normalized transverse emittance of the bunch head after it is output from the ECITC RF gun are interpreted reasonably, and the corresponding slice simulations are also performed to validate this interpretation. In summary, the first emittance minimum, which appears in close proximity to the location of the minimum beam radius, is induced by the effect of the equivalent focusing lens of the accelerating cavity. Also, because reconfiguration of the charge to produce a uniform density is a ubiquitous process in single-component plasmas, of which high-density electron beams are a prime example, the second emittance minimum is observed away from the first minimum. On the basis of the analysis above, the prospects of the assembly scheme for the HUST THz-FEL injector are assessed. In this process, both the longitudinal and transverse properties of the bunch are considered synthetically, and the beam dynamics of the joint-debugging process with the subsequent equipment indicate that optimal location of the booster linac
Rev. Sci. Instrum. 85, 103302 (2014)
and the surrounding focusing coils can ensure that the bunch will be accelerated immediately when its radius reaches the focal point, which means that the beam brightness will not be diluted before transmission to the linac. Consequently, when considering its flexibility and robustness, the use of the optimized EC-ITC RF gun to ease the trade-off between high performance and compact structure for high-power table-top THz-FELs is a highly attractive prospect. ACKNOWLEDGMENTS
The authors would like to thank Professor Dezhi Chen for assistance with writing this paper. This work was funded by the National Nature Science Foundation of China (Grant No. 11375068) and the 2011 project - Hubei Collaborative Innovation Center for Non-power Nuclear Technology. 1 S.
Krishnagopal and V. Kumar, Radiat. Phys. Chem. 70, 559–569 (2004). G. Biedron, J. W. Leweelen, S. V. Milton et al., “Compact highpower electron beam based terahertz sources,” Proc. IEEE 95, 1666–1678 (2007). 3 P. Tan, J. Huang, K. F. Liu, Y. Q. Xiong, and M. W. Fan, Sci. China: Inf. Sci. 55, 1–15 (2012). 4 T. Shintake, H. Matsumoto, T. Ishikawa, and H. Kitamura, Proc. SPIE 4500, 12–23 (2001). 5 K. Togawa, H. Baba, K. Onoe, T. Inagaki, T. Shintake, and H. Matsumoto, Nucl. Instrum. Methods Phys. Res. A 528, 312 (2004). 6 K. Togawa, T. Shintake, T. Inagaki, K. Onoe, T. Tanaka, H. Baba, and H. Mastsumoto, Phys. Rev. Spec. Top.–Accel. Beams 10, 020703 (2007). 7 T. Hara, K. Togawa, H. Tanaka, T. Hasegawa, Y. Kana, T. Morinaga, and Y. Tajiri, Proceedings of the 2011 Free Electron Laser Conference, Shanghai, China, 2011, http://www.jacow.org, pp. 255–258. 8 H. Tanaka, Proceedings of IPAC’2012, New Orleans, Louisiana, USA, 2012, http://www.jacow.org, pp. 2106–2110. 9 T. Tanaka, F. Hinode, M. Kawai, and H. Hama, Proceedings of the 27th International Free Electron Laser Conference, California, USA, 2005, http://www.jacow.org, pp. 1–6. 10 J. W. Lewellen, Proceedings of the 2003 Particle Accelerator Conference, Oregon, USA, 2003, http://www.jacow.org, pp. 2035–2037. 11 H. Hama, M. Yasuda, M. Kawai, F. Hinode, K. Nanbu, and F. Miyahara, Nucl. Instrum. Methods Phys. Res. A 637, S57–S61 (2011). 12 Y. J. Pei, J. Pang, K. Jin, G. Y. Feng, L. Shang, S. K. Lu, Y. L. Hong, G. R. Hong, and D. C. Jia, Proceedings of IPAC’10, Kyoto, Japan, 2010, http://www.jacow.org, pp. 1737–1739. 13 Y. J. Pei, J. Pang, G. Y. Feng, S. K. Lu, L. Shang, K. Jin, Y. L. Hong, G. R. Huang, D. C. Jia, and M. W. Fan, China patent CN101778527B (2010). 14 T. N. Hu, Y. J. Pei, B. Qin, and Q. S. Chen, Chin. Phys. C 37, 128101 (2013). 15 B. Qin, P. Tan, L. Yang, and Xialing Liu, Nucl. Instrum. Methods Phys. Res. A 727, 90–96 (2013). 16 T. N. Hu, Q. S. Chen, Y. J. Pei, J. Li, and B. Qin, “Physical design of FEL injector based on performance-enhanced EC-ITC RF gun,” Chin. Phys. C 37, 018101 (2014). 17 M. J. Van Der Weil, see http://www.asianscientist.com/books/wp-content/ uploads/2013/06/4524_chap01.pdf (2013). 18 R. H. Miller et al., IEEE Trans. Nucl. Sci. 32, 3231 (1985). 19 X. Sun, Y. Yang, and Y. Lin, Proceedings of the 1st Asian Particle Accelerator Conference, Tsukuba, Japan, 1998, http://www.jacow.org, p. 184. 20 H. Yang, S. H. Kim, S. J. Park, J. S. Oh, M. Cho, and W. Namkung, Nucl. Instrum. Methods Phys. Res. A 703, 145–151 (2013). 21 X. Z. He, C. X. Tang, W. H. Huang, and Y. Z. Lin, Nucl. Instrum. Methods Phys. Res. A 560, 197–203 (2006). 22 Z. Huang, Y. Ding, and J. Qiang, Nucl. Instrum. Methods Phys. Res. A 593, 148–151 (2008). 23 J. B. Rosenzweig, A. M. Cook, R. J. England, M. Dunning, S. G. Anderson, and M. Ferrario, Nucl. Instrum. Methods Phys. Res. A 557, 87–93 (2006). 24 K. Kusoljariyakul and C. Thongbai, Nucl. Instrum. Methods Phys. Res. A 645, 191–196 (2011). 25 B. E. Carlsten, Nucl. Instrum. Methods Phys. Res. A 285, 313 (1989). 2 S.
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 103302 (2014)
Study of beam transverse properties of a thermionic electron gun for application to a compact THz free electron laser Tongning Hu,1,a) Yuanji Pei,2,a) Bin Qin,1 Ping Tan,1 Qushan Chen,1 Lei Yang,1 and Ji Li2 1 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074, China 2 National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, China
(Received 9 December 2013; accepted 27 September 2014; published online 13 October 2014) A novel thermionic electron gun adopted for use in a high power THz free electron laser (FEL) is proposed in this paper. By optimization of the structural and radiofrequency (RF) parameters, the physical design of the gun is performed using dynamic calculations. Velocity bunching is used to minimize the bunch’s energy spread, and the dynamic calculation results indicate that high quality beams can be provided. The transverse properties of the beams generated by the gun are also analyzed. The novel RF focusing effects of the resonance cavity are investigated precisely and are used to establish emittance compensation, which enables the injector length to be reduced. In addition, the causes of the extrema of the beam radius and the normalized transverse emittance are analyzed and interpreted, respectively, and slice simulations are performed to illustrate how the RF focusing varies along the bunch length and to determine the effects of that variation on the emittance compensation. Finally, by observation of the variations of the beam properties in the drift tube behind the electron gun, prospective assembly scenarios for the complete THz-FEL injector are discussed, and a joint-debugging process for the injector is implemented. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4897481] I. INTRODUCTION
Among the diverse range of available terahertz (THz) sources, free electron lasers (FELs) have been the focus of recent research interest because of their distinct merits, such as high power and continuously tunable radiation.1, 2 For commercial and civil use, apart from high average power requirements, low costs and compact structures must also be considered. Cost-effective FELs with linear accelerator injectors have the potential to achieve a balance among these conditions.3 With its high stability and long lifetime, the conventional injector system using a thermionic cathode followed by a buncher system has been applied widely.4–6 With the benefits of many modifications and upgrades, the thermionic injector used in the SPring-8 Angstrom Compact Free Electron Laser (SACLA)7 has achieved improved beam performance: the emittance value is maintained at around 1π mm · mrad, and the resulting beam charge increased up to 250 pC.8 However, the subharmonic buncher and the long drift section contained therein preclude reduction of the device size, which is essential for widespread distribution of THz sources. Also, recent research indicates that a thermionic electron gun with two independent tunable cavities (ITCs)9 can produce a more compact injector layout by using velocity bunching to minimize the energy spread.10, 11 In addition, the back bombardment effect is eliminated almost completely by implementation of an external cathode (EC),12, 13 and the insufficient a) Authors to whom correspondence should be addressed. Electronic ad-
dresses: [email protected] and [email protected]
0034-6748/2014/85(10)/103302/8/$30.00
charge bottleneck can also be overcome by optimizing the dimensions and the RF parameters of the ITC cavities.14 After careful consideration, the EC-ITC radiofrequency (RF) gun has been adopted for use in the THz-FEL oscillator proposed by Huazhong University of Science and Technology (HUST) in combination with University of Science and Technology of China (USTC),15 which aims to generate 50 – 100 μm coherent radiation with 1 MW-level peak power on a table-top scale. In the conceptual design, the injector mainly consists of the EC-ITC gun and a booster linac coupled to focusing coils;16 the corresponding scheme for the injector is shown in Fig. 1. According to the formula used to define beam brightness,17 the transverse parameters of the bunch, such as the beam radii and the transverse emittance, must be confined within an acceptable scale. Previous research on the standing-wave cavity has shown that the RF focusing of the cavity itself seems to serve the purpose of beam cross-section compression,18 and that the RF focusing can be enhanced by a higher accelerating gradient, which is usually limited by the power of the available RF sources and the breakdown field strengths of the cavities. Sun et al.19 proposed an approach using asymmetric RF fields to enhance the RF focusing and RF phase focusing (transverse RF focusing that depends on the beam phase); this approach has been validated by the latest beam dynamics,20 and the results agree effectively with test results. Another intrinsic drawback of the thermionic electron gun is its considerable transverse emittance, which conflicts with the requirements of the HUST THz-FEL. To a certain extent, the concepts of emittance growth and compensation of photocathode injectors are of sufficient significance to be used
85, 103302-1
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FIG. 1. Schematic view of the HUST THz-FEL injector.
for reference here, because of the in-depth studies that have been performed and the various solutions offered by these studies.21–24 Although the physical design of the enhanced EC-ITC RF gun has been performed and the simulation results fulfill the design targets, the elaborate transverse properties must still be investigated using slice simulations, and the effects of RF focusing on emittance compensation must also be explored more intensively. Additionally, further studies of the injector assembly scheme are still necessary, and will have a significant impact on the scale of the facility. This paper will address all the above subjects. II. PHYSICAL DESIGN OF THE EC-ITC RF GUN
As mentioned above, the intrinsic drawbacks of ordinary thermionic electron guns, and particularly the insufficient bunch charge, can be overcome using the EC-ITC RF gun. Based on multi-cavity RF gun theory, the four main design criteria of the EC-ITC RF gun are summarized as follows. (1) The drift tube length L between the two cells must be sufficient to attenuate the electric field strength EL , which is supposed to be 0.1% of the peak value E0 . The relational expressions are listed as follows: EL = e−αL , E0 2π α= λ
2.405λ 2π b
(1)
2 − 1,
(2)
where α is the attenuation constant, λ is the RF wavelength, and b is the drift tube radius. (2) Because the relative velocity of the synchronous electron β e < 1, the length Li of the ith cell of the ITC should be set appropriately in non-relativistic cases, λ Li = βpi , 2
FIG. 2. (a) Two-dimensional sketch of the ITC with field distributions and chamfer illustration, and (b) three-dimensional sketch of the ITC with couplers and plunger.
ments indicated that the ITC is not in danger of reaching its breakdown field strength.12 (4) Two input couplers are applied to supply power independently to the two cells of the ITC and are assembled vertically to avoid spatial conflicts. A plunger is inserted into Cell 1 for frequency tuning. A three-dimensional drawing of the ITC with the couplers and plunger is shown in Fig. 2(b). In the design of the HUST THz-FEL injector, a gridded electron gun with double anodes is adopted as the beam source and can produce a 5 A, 15 keV DC beam with 1 mm waist radius and a 42 mm shot range,14 and the subsequent ITC is implemented to extract a micro-bunch train with high brightness. By adjusting the cavity dimensions and the RF parameters in Superfish and Parmela simulations, the optimal output states of the EC-ITC RF gun are derived as shown in Fig. 3, while the specific bunch performance and RF parameters are listed in Table I. During the simulation, OPERA/CST is used to generate the beam distribution from the electron gun,14 and the peak electrical field strengths of the two cells are 40.45 MV/m and 89.28 MV/m. When output from Cell-1 of the EC-ITC RF gun, the beam kinetic energy obtained is 442 keV, the bunching process is almost complete and the micro-bunch head contains a charge of over 200 pC. This shows that the HUST THz-FEL injector, which has a more compact layout, can produce a performance similar to that of the SACLA injector. Additionally, because of the low energy spread of the ITC gun, the elongation of the bunch extracted from Cell-2 can be ignored within a short range, and the longitudinal properties will therefore not be concentrated thereafter. However, the transverse properties of Cell-2, such as the radius and the emittance, must be analyzed and discussed emphatically with regard to their contributions to the final beam brightness.
(3)
where β pi is the equivalent phase velocity of the ith cell, and obeys the identity β ei ≡ β pi . (3) To avoid cutting burrs during machining, simple external arcs are used rather than nose cones, and a 0.03 mm interspace is reserved for diamond tool return, as illustrated in Fig. 2(a). Additionally, artificial machine tools are adopted rather than numerically controlled machine tools, so that the effects of the machining accuracy can be reduced. Under these conditions, previous experi-
III. TRANSVERSE FOCUSING OF CELL-2 IN THE EC-ITC RF GUN
By consideration of the overall system requirements, the field configuration and the input beam parameters of the ECITC RF gun have already been determined. However, because of the defocusing forces that are induced by the RF fields and the space-charge field, the extracted high current and low energy beams are subjected to detrimental effects on their transverse beam sizes, and RF phase focusing has been
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FIG. 3. Output states of the EC-ITC RF gun: (a) Phase spectrum; (b) transverse spot; (c) longitudinal phase space; and (d) energy spectrum.
shown to have the potential for beam envelope refinement. Because Cell-2 can be regarded as a focusing lens, analysis of the equivalent focusing properties has significance for the assembly positions and the design targets of the downstream equipment. A. Focusing properties of super-short bunches
In the case of axisymmetric standing-wave cavities operating in the TM010 mode, only the radial force contributes to
Beam energy Micro-bunch head charge Micro-bunch length (FWHM), σ z Energy spread (FWHM) Normalized emmittance, n Micro-bunch radius (rms) Micro-bunch repetition rate Macro-pulse current Macro-pulse duration Macro-pulse repetition rate
where r is the radial position, and β is the electron speed as a proportion of the light speed c. The longitudinal electric field along the z axis can be expressed as Ez (z, t) = Ez (z) cos(kct + φ0 )
TABLE I. Main EC-ITC RF gun parameters. Parameter
the radial motion of the internal electrons. On the basis of the Maxwell equations, by taking only the first order of the transverse electromagnetic fields into account and by using the approximate condition z˙ = βc, the radial force can be written as ∂Ez (z, t) er ∂Ez (z, t) β − × , (4) Fr = − 2 ∂z c ∂t
Value 2.6 MeV 201 pC 1.5 ps 0.27% 6.5π mm · mrad 0.9 mm 2856 MHz 0.574 A 4-6 μs 10–200 Hz
= Em sin
kz cos(kct + φ0 ). βp
(5)
Here, t is the electron injection time related to the synchronous electron, φ 0 is the synchronous electron phase, and Em is the axial electrical field amplitude. We assume that the injected bunch has an infinitesimal length and that its radius is sufficiently small such that the transverse component of the energy spread can be neglected. Additionally, the bunch is always on the crest of the RF field, which means that the bunch with the centered synchronous electron can be called the synchronous slice. Meanwhile, the slices located in front of and behind the RF crest can be
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By substituting Eq. (6) into Eq. (4), and using k = 2π /λ and β p = 2L/λ, a simplified expression for Fr can be written as π π erEm cos z . (7) Fr = − 2L L Based on Eq. (7), the radial motions of the synchronous slice are determined as follows: (1) In the first part of the cavity, z ∈ [0, L/2], Fr < 0, and thus the synchronous slice is subjected to a focusing effect. (2) In the second part of the cavity, z ∈ [L/2, L], Fr > 0, and thus the synchronous slice is subjected to a defocusing effect. (3) Fr is proportional to Em . To provide intuitive demonstrations of the focusing properties of Cell-2, a simulated cylindrical bunch with a uniform density distribution and a super-short length is used as the input to Cell-2. By selecting the same peak electric field strength value as that mentioned in Sec. II, and by tuning the RF field phase to ensure that the input bunch will be on the crest of the accelerating electrical field, the variations in the transverse size σ x along the z axis under different field strengths have been plotted in Fig. 4, where the starting position is the entrance to Cell-2. Obviously, after entering the main cavity (z = 1.8 cm ∼ 4.524 cm) of Cell-2, the super-short bunch is subjected to a strong focusing effect in the first half of the cavity and a weak defocusing effect in the second half of the cavity. Because the former effect is dominant, the focusing trend only slows in the second half of the cavity, and the beam output from Cell-2 (z = 6.5 cm) continues focusing until it reaches the focal point in the later drift tube. Additionally, the focusing effect becomes stronger under higher electric 2.5
67.0MV/m, without space−charge 89.3MV/m, without space−charge 111.9MV/m, without space−charge 67.0MV/m, with space−charge 89.3MV/m, with space−charge 111.9MV/m, with space−charge
σx (mm)
2 1.5
0.5 5
10 z(cm)
15
(a)
15
20
FIG. 4. σ x variations along the z axis with different peak electric field values.
without space−charge with space−charge
10 5 0
70
80
90
100 110 Em (MV/m)
120
130
140
0.2 without space−charge with space−charge (b)
0.15 0.1 0.05 0
70
80
90
100 110 Em (MV/m)
120
130
140
FIG. 5. (a) Focusing length variations and (b) focal radius variations of Cell-2 of the EC-ITC RF gun.
fields, which is in turn evidence for the third conclusion drawn from Eq. (7). In addition, Fig. 5 shows how Em affects the focal length and the focal radius, while the space-charge field plays a subdued role for both of these parameters. However, the effects of the space-charge field will saturate when Em > 140 MV/m, as shown in Fig. 5, because the electron beams approach the speed of light. B. Focusing properties of bunches with finite lengths
In the qualitative analysis of the radial motion and beam dynamics of the synchronous slice in Subsection III A above, several approximate conditions are applied and the conclusion of the general focusing trend of the super-short bunches at the optimal acceleration phases is derived. However, in view of the actual situation of bunches with finite lengths, the internal slices at different longitudinal positions are subjected to the different radial forces induced by the RF phase differences that they encounter, meaning that the time dependence of the RF fields must be taken into account. Using the differ∂Ez (z,t) ∂E (z,t) dz + z∂t dt, Eq. (4) can ential operator dEz (z, t) = ∂z be transformed into Fr = −
1
0 0
20
Focal length (cm)
defined as advancing slices and lagging slices, respectively. The synchronous slice always matches the axial electrical field amplitude in the accelerating cavity, which means that the time dependence of the RF fields can be neglected, and Eq. (5) can be simplified as Ez (z, t) = Em sin (kz/β p ). Therefore, the approximate conditions can be obtained as follows: ⎧ ∂Ez (z, t) ⎪ ⎪ =0 ⎨ ∂t (6) π ⎪ ∂Ez (z, t) π Em ⎪ ⎩ = cos z . ∂z L L
Focal radius (mm)
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er dEz (z, φ) ker ∂Ez (z, φ) + , 2 dz 2βγ 2 ∂φ
(8)
where γ is the relativistic factor, and Ez (z, t) is replaced by Ez (z, φ) by using φ = kct + φ 0 , where φ is the electron phase related to the synchronous electron. The first term on the right-hand side of Eq. (8), FI dE (z,φ) = − er2 zdz is the total derivative of the longitudinal electric fields along the electron trajectory, which act as an electrostatic lens.18 The second term, FII , determines the RF phase focusing force,19 which will be the focus of study here and
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can be expressed as
with constant energy in free space, it is more convenient to replace the physical phase space with a geometric phase space; meanwhile, the rotation between the horizontal and vertical phase spaces of the axially symmetrical bunches are very much alike, and thus the normalized transverse emittance can be defined by Eq. (10):
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FI I = =
ker ∂Ez (z, φ) 2βγ 2 ∂φ ker πz cos φ. sin 2 2βγ L
(9)
Because sin πz consistently remains positive in the cavL ity, the sign of FII depends on cos φ. The function of FII on the beam radial motion can be concluded as follows: (1) In the case of advancing slices, φ ∈ (0, π /2), FII > 0 and acts as a defocusing force. (2) In the case of lagging slices, φ ∈ (π /2, π ), FII < 0 and acts as a focusing force. (3) FII does not affect the synchronous slice (φ = π /2), which is time-independent. To inspect the focusing effect, including RF phase focusing in Cell-2, an initial 200 pC, 442 keV beam with width of 40◦ is launched in Parmela; the beam has the same shape and distributions as the ultra-short bunch described in Subsection III A. The theoretical derivation is confirmed by the beam dynamic results shown in Fig. 6(a), while Fig. 6(b) indicates that the advancing beams are bunched while lagging beams are debunched. Although stronger transverse focusing can be obtained by placing more electrons behind the RF crest, the bunch elongation cannot be ignored for the HUST THz-FEL injector. IV. EMITTANCE COMPENSATION
The beam emittance is the region in phase-space that is occupied by the particles in a beam.25 For electrons
n,x =
N
xi2
i=1
N
xi2 −
N
i=1
2 xi xi
.
(10)
i=1
According to previous researchers, the transverse emittance can be simply classified into two typical types, the projected emittance and the slice emittance, and the former is conventionally discussed in emittance compensation. Several approaches have been suggested for emittance minimization, including use of a solenoid magnet, RF radial focusing, use of alternative cathode materials and design of a specific RF gun.24 While the concept of emittance compensation is generally discussed for photocathode guns for short-wavelength radiation applications, the issue of emittance growth has yet to be settled for high brightness injectors like the HUST THzFEL injector, and thus Hu et al.16 introduced a standard emittance compensation scenario using a short magnetic lens and focusing coils, which are inevitably accompanied by loss of system compactness. A. Beam emittance of the EC-ITC RF gun
To be as close to the real situation as possible, a cutoff head from the bunch extracted by the EC-ITC RF gun is used, which is the same condition as that of Sec. II. After drifting in free space, the transverse property variations of the bunch head are given in Fig. 7. 2.5
4 advancing bunch synchronous bunch lagging bunch
2
(a)
3.5
σx (mm)
σz (mm)
N βγ
with space−charge without space−charge (a)
1.5 1
3
0.5 2.5
2
4
6
8
10 12 z(cm)
14
16
18
0 0
20
with space−charge without space−charge
advancing bunch synchronous bunch lagging bunch
mrad)
(b)
2
n,x (mm
σx (mm)
40
60 z(cm)
80
100
120
80
100
120
8
3 2.5
20
1.5 1
7
(b)
6 5
0.5 0 0
5
10 z(cm)
15
20
FIG. 6. (a) σ x variations and (b) σ z variations along the z axis for the different phases.
4 0
20
40
60 z(cm)
FIG. 7. (a) Transverse size (rms) variations and (b) normalized transverse emittance (rms) variations of the EC-ITC RF gun along the z axis.
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FIG. 8. Longitudinal profiles [(a), (b), (c)] and transverse phase spaces [(d), (e), (f)] of the bunch head at the exit of the EC-ITC RF gun, the position of the first minimum of σ x and the position of the second minimum of σ x , respectively.
The beam envelope continues to decrease in free space until it is more than 40 cm away from the exit of Cell-2, as shown in Fig. 7(a); this is caused by the focusing effect of Cell-2. Observation of Fig. 7(b) indicates that, under space-charge effects, two minimal values for the normalized transverse emittance n, x are explored in free space. By borrowing the concept of emittance compensation from photocathode guns, the beam reconfigurations can be interpreted as follows: (1) The effect of the equivalent focusing lens of Cell-2 acts as a conventional approach for projected emittance compensation, and the first minimum of n, x is obtained near the focal point; the corresponding bunch profile and the transverse phase space are shown in Figs. 8(b) and 8(e), respectively. (2) Because of its internal particle distribution, the extracted bunch evolves through the spatial expansion of differing radii to achieve a quasi-ellipsoidal formation, which then has a linear space-charge field on all spatial coordinates.23 This is similar to the temporal shaping technique of driven laser pulses that is used in photocathode injectors. The bunch (x, z) distributions at various positions in the subsequent drift tube are clearly displayed in Figs. 8(a)–8(c). Here, the beam has 2.6 MeV mean energy, and its transverse dynamics are spacecharge dominated. An “inflated” ellipsoidal beam shape can clearly be seen in Fig. 8(c), which is obtained purely from space-charge effects. The second minimum of n, x is therefore obtained as shown in Fig. 7(b), while the corresponding transverse phase space is displayed in Fig. 8(f).
B. Slice simulations for the EC-ITC RF gun
To show how the RF focusing varies along the bunch length and the effect of that variation on emittance compensation, slice simulations must be implemented for Cell-2. In the simulation, the bunch extracted from Cell-1 is divided into several slices with widths of 1 ps in the longitudinal direction. Apparently, the transverse properties of the slices vary differently from each other along the z axis, as shown in Fig. 9. While the initial transverse properties of the slices are different to each other, it is clear that the focusing capability of a lagging slice is much stronger than that of an advancing slice, as shown in Fig. 9(b), which is similar to the result concluded in Subsection III B. Also, Fig. 9(a) shows that the emittance of the lagging slice changes more slowly than that of the advancing slice. Therefore, addition of more particles to the lagging phase helps to strengthen the effects of RF phase focusing of Cell-2 on emittance compensation. V. ASSEMBLY OUTLOOK
For the future assembly of the HUST THz-FEL, apart from the basic compactness requirement, several other aspects must be considered for the injector assembly scenario, which are described as follows: (1) Adequate space must be reserved for a toroid at a downstream location of the EC-ITC RF gun for beam testing. (2) The bunches generated by the EC-ITC RF gun must enter the booster linac as quickly as possible to guarantee that their properties will not degrade sharply. (2) To resolve the contradiction above, a drift tube must be used between the EC-ITC RF gun and the booster
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10
1.1
advancing slice synchronous slice 1st lagging slice 2nd lagging slice 3rd lagging slice
with space−charge without space−charge
1
(a) σz (mm)
n,x (mm mrad)
15
5
(a)
0.9 0.8 0.7
0 0
20
40
60 z(cm)
80
100
120
0.6 0
2.5
1.5
5
advancing slice synchronous slice 1st lagging slice 2nd lagging slice 3rd lagging slice
Energy spread(rms)
σx (mm)
2
(b)
1 0.5 0 0
20
40
60 z(cm)
20
40
−3
80
100
120
x 10
4
with space−charge without space−charge
60 z(cm)
80
100
120
80
100
120
(b)
3 2 1 0 0
20
40
60 z(cm)
FIG. 9. (a) n, x variations and (b) σ x variations of the different slices in the bunch extracted from the EC-ITC RF gun.
FIG. 10. (a) Longitudinal length (rms) variations and (b) energy spread (rms) variations of the EC-ITC RF gun along the z axis.
linac, while associated focusing magnets must be used simultaneously around the tube and the subsequent linac for radial compression and suppression of emittance growth. (3) To prevent the deflection effects of the magnetic fields acting on low-energy electrons, the focusing coils must be located away from both the cathode and Cell-1.
Depending on the beam dynamics in the EC-ITC RF gun and the subsequent drift tube, the first minimum of n, x is clearly located at a position 34 cm away from the exit of the gun, and the minimum of σ x appears later, 46 cm away from the exit of the gun, as shown in Fig. 7. Additionally, the variations of both the bunch length and the energy spread are shown in Fig. 10, which indicates that both of the longitudinal properties only degrade slightly up to 25 cm away from
FIG. 11. Beam property variations along the beamline after the EC-ITC RF gun: (a) transverse size, (b) normalized transverse emittance, (c) energy spread, and (d) bunch length.
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the exit of the gun, but deteriorate rapidly later; a position near the transition point might therefore be suitable for the entrance to the linac. Based on numerous optimizations, the optimal assembly positions for the booster linac and the associated focusing coils are determined, and these positions are validated by start-to-end dynamic calculations. The property variations in the downstream drift tube and the linac are shown in Fig. 11, which indicates that the injector assembly scenario fulfills the compact structure and high performance requirements. While the short magnetic lens around the drift tube in the original focusing scheme16 can be avoided, adequate space is still reserved for this lens in case it is required for uncertain operations. VI. DISCUSSION AND CONCLUSIONS
The physical design of the EC-ITC RF gun to be used for the FEL injector is conducted using the PARMELA code, and the space-charge effects are calculated using the SCHEFF routine in PARMELA. According to the beam dynamics results, high quality bunches with effective charge of over 200 pC can be obtained using this type of injector. Compared with traditional thermionic guns, the EC-ITC RF gun adopted here can overcome notable problems, such as high energy spread and high transverse emittance, while having a compact and robust structure, unlike complex photocathode RF guns. In other words, the EC-ITC RF gun fulfills the requirements for use in the HUST THz-FEL. For confinement of the beam radius, the RF focusing and RF phase focusing of Cell-2 of the EC-ITC RF gun are carefully analyzed, and the cell dimensions are refined. In addition, the beam dynamics indicate that the space-chargedominated relativistic beam extracted by the EC-ITC RF gun is not subjected to transverse beam profile expansion before entering the linac. This means that Cell-2 plays a role in RF focusing, which can then release the space occupied by the magnetic lens in the original assembly scenario. In addition, by borrowing the conceptual framework from previous works in the context of emittance growth and compensation in photocathode guns, the variations in the normalized transverse emittance of the bunch head after it is output from the ECITC RF gun are interpreted reasonably, and the corresponding slice simulations are also performed to validate this interpretation. In summary, the first emittance minimum, which appears in close proximity to the location of the minimum beam radius, is induced by the effect of the equivalent focusing lens of the accelerating cavity. Also, because reconfiguration of the charge to produce a uniform density is a ubiquitous process in single-component plasmas, of which high-density electron beams are a prime example, the second emittance minimum is observed away from the first minimum. On the basis of the analysis above, the prospects of the assembly scheme for the HUST THz-FEL injector are assessed. In this process, both the longitudinal and transverse properties of the bunch are considered synthetically, and the beam dynamics of the joint-debugging process with the subsequent equipment indicate that optimal location of the booster linac
Rev. Sci. Instrum. 85, 103302 (2014)
and the surrounding focusing coils can ensure that the bunch will be accelerated immediately when its radius reaches the focal point, which means that the beam brightness will not be diluted before transmission to the linac. Consequently, when considering its flexibility and robustness, the use of the optimized EC-ITC RF gun to ease the trade-off between high performance and compact structure for high-power table-top THz-FELs is a highly attractive prospect. ACKNOWLEDGMENTS
The authors would like to thank Professor Dezhi Chen for assistance with writing this paper. This work was funded by the National Nature Science Foundation of China (Grant No. 11375068) and the 2011 project - Hubei Collaborative Innovation Center for Non-power Nuclear Technology. 1 S.
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