On the suitability of longitudinal profile measurements using Coherent Smith-Purcell radiation for high current proton beams
Joanna Barros, Nicolas Delerue, Mélissa Vieille-Grosjean, Irena Dolenc Kittelmann, Cyrille Thomas
OOn the suitability of longitudinal profilemeasurements using CoherentSmith-Purcell radiation for high currentproton beams ∗ J. Barros † , N. Delerue, M. Vieille-Grosjean, LAL, Orsay, FranceI. Dolenc Kittelmann, C. Thomas, ESS, Lund, Sweden Abstract
The use of Smith-Purcell radiation to measure electrons longitudinal profiles has beendemonstrated at several facilities in the picosecond and sub-picosecond range. Thereis a strong interest for the development of non intercepting longitudinal profile diag-nostics for high current proton beams. We present here results of simulations on theexpected yield of longitudinal profile monitors using Smith-Purcell radiation for suchproton beams.
Handling high current proton beams is a challenge for beam diagnostics in fu-ture proton accelerators. In order to achieve a high beam power, it is mandatoryto understand the beam dynamics and to determine the beam size and profilewith precision. In high power proton Linacs, such understanding would allow afull characterization of the beam after each Linac section. With a beam trans-verse size of 2 to 3 mm, intercepting profile diagnostics such as OTR screens orCherenkov monitors can be used only during tuning and specific beam opera-tion modes. To determine the longitudinal profile, Feschenko-type Bunch ShapeMonitors (BSM [1]) can be used in the low energy sections of the Linac, how-ever, BSM may not be sensitive to short bunch lengths. In the higher energysections, it is highly advisable to use non interceptive devices to avoid radiationsor damage to the equipment. Wall current monitors or other methods basedon detecting the fields at the vacuum chamber boundary could be used, butthey are intrinsically limited in resolution due to the rather low relativistic β [2] and do not have an adapted temporal resolution. Therefore, a diagnosticbased on Smith-Purcell radiation could be of high interest. We will investigatehere the possibility of using a Smith-Purcell diagnostic for the measurement ofproton beams longitudinal profiles, using a numerical simulation code presentedhereafter. ∗ Work financially supported by the Universit´e Paris-Sud (programme ”attractivit´e”) andthe French ANR (contract ANR-12-JS05-0003-01) † [email protected] a r X i v : . [ phy s i c s . acc - ph ] J u l description of the simulation Fig. 1:
Coordinate system used for the simulation
Smith-Purcell radiation can be described by the ”surface current” theory [4]:when charged particles travel over a grating, they induce an image charge onits surface and keep pace with it. The corrugations of the grating cause thecreated current to accelerate, which in turn leads to the emission of radiation.In our coordinate system, we assume that the protons travel perpendicularly tothe grooves of a blazed grating. Due to the periodic structure of the grating,the emitted wavelength λ depends on the observation angle θ defined in Fig. 1.The grating shape and pitch defines its efficiency, that varies depending on θ and on the second observation angle called φ .Our simulation describes the Smith-Purcell intensity radiated per unit solidangle for a single particle, as described in the equation (2a) of [3] for a gratingof period l and length Z positioned at a distance x from the beam center: (cid:18) dId Ω (cid:19) = 2 πq Zln λ R exp (cid:34) − πx λ (cid:112) β γ sin θsin φβγ (cid:35) (1)The term R represents the grating efficiency that contains the contributionfrom each period of the grating, and is different for each grating shape [5]. Herewe use echelette gratings whose efficiency will be shown in the Results section.For a given bunch of N P particles, the emitted radiation has a high degreeof coherence when the radiation wavelength is comparable to the bunch length.In the equation (2), S coh. and S incoh. represent the coherent and incoherentcomponents of the emitted radiation respectively. Assuming that the transverseand longitudinal profiles are not correlated, S coh. can be expressed as the prod-uct two functions T and G encoding the longitudinal (temporal) and transverseprofile respectively. σ x and σ y are the beam dimensions in x and y directions,and ω is the frequency. (cid:18) dId Ω (cid:19) N P = (cid:18) dId Ω (cid:19) ( N P S incoh. + N P S coh. ) (2) choice of measurement parameters S coh. = (cid:12)(cid:12)(cid:12)(cid:12)(cid:90) ∞−∞ T e − iωt dt (cid:12)(cid:12)(cid:12)(cid:12) G ( σ x , σ y ) (3)In the case where the coherent component prevails, the emitted radiationencodes the form factor of the bunch and its measurement allows to recoverinformation about the bunch longitudinal profile. If we assume that the beamis gaussian in the transverse plane and G is normalized to 1, then the emittedenergy is proportional to the form factor as shown in 4. (cid:18) dId Ω (cid:19) N P (cid:39) (cid:18) dId Ω (cid:19) N P (cid:12)(cid:12)(cid:12)(cid:12)(cid:90) ∞−∞ T e − iωt dt (cid:12)(cid:12)(cid:12)(cid:12) (4)This form factor corresponds to the modulus of the Fourier transform ofthe temporal profile. In order to recover the full profile the phase needs to bereconstructed. Several techniques are possible, and are documented in [7].In this work, we use a code package written by G. Doucas [3], that takesseveral beam parameters as an input and generates the a Smith-Purcell spec-trum, which is a calculation made from the Fourier transform of the temporalprofile and chosen grating parameters. The parameters used for this study on proton beams are summarized in Table1. We assume that the beam transverse dimensions would allow approaching agrating at a distance x = 10 mm from the beam center. Tab. 1:
Used beam parameters for the simulation
Parameter Unit Value γ - ≈ β - 0.92Transverse x size (FWHM) mm 2Transverse y size (FWHM) mm 2Number of protons per bunch - 1 × Expected bunch length (FWHM) ps 3Number of bunches per train - 1 × Frequency MHz 352Repetition rate Hz 14
The choice of suitable grating parameters is made by first taking into accountthe preferred geometry for detection. Here we chose to maximize the signalat θ =90 ° . Our optics collect light with a high numerical aperture, so that thesignal generated by the code will be integrated over the whole captured solidangle. The optics are placed at 200 mm from the grating, and the opening ofthe detection cone is 100 mm to increase the incoming signal on the detectors. Results The grating pitch is selected in order to make sure that the emission is mostlyin the coherent regime, so that the measurement would be sensitive to the beamlongitudinal profile (see Eq. (2)). The increase in signal seen on Fig. 2 whenthe grating pitch increases, corresponds to the onset of the coherent component.We chose a value of the grating period that is a trade-off between the differentangles to ensure a good sensitivity at all angles: the three angular componentsare in the coherent range. Keeping in mind that the insertion length needs tobe as small as possible, and that we would prefer the maximum of the signalto be at 90 ° , we chose a grating period of 13 mm. The grating parameters aresummarized in Table 2. E ne r g y pe r bun c h ( n J ) Theta=60° Theta=90° Theta=120°
Fig. 2:
Evolution of the Smith-Purcell signal with different grating pitches.
Tab. 2:
Grating parameters for the simulation
Parameter Value
Width 40 mmNumber of periods 15Blaze angle 30 ° Pitch 13 mm
Knowing the expected signal level, it is now necessary to verify that the device issensitive to a longitudinal profile change, which is a crucial feature for a profilemeasurement tool. The sensitivity to a variation in the bunch FWHM lengthis shown in Fig. 3 for the chosen grating and optics parameters. The coher-ent emission becomes progressively predominant as the bunch length decreases,which leads to a significant and measurable signal increase. This is shown inFig. 3, where the wavelength at θ = 90 ° varies by more than 20% for a bunchlength varying from 3 to 10 ps, but a similar change is also observed at otherwavelengths showing a significant change of the power spectrum distribution. Conclusion E ne r g y pe r bun c h ( n J ) Theta=60° Theta=90° Theta=120°
Fig. 3:
Simulated Smith-Purcell signal for a 13 mm grating depending on thebunch length.The signal level for the simulated case, as shown in Fig. 3, is of the orderof 1 nJ per bunch, and needs to be compared with the performances of thedetectors used. For example, if the detectors measure an averaged signal overseveral ms, which is the case of the pyroelectric sensors often used in experimentsinvolving electrons [6], they will detect the Smith-Purcell power produced bya whole train (around 1 × bunches), thus a higher signal by several ordersof magnitude, up to mJ. However, these values do not take into account thetransmission of the different optical elements that would need to be installedin front of the detectors. Also, as seen in Fig. 4, the expected Smith-Purcellemission would occur in the millimeter-wave range where the background levelneeds to be evaluated to be able to distinguish it from the actual signal. If weuse detectors that are sensitive only to signal variations, they will not impactedby the effect of the temperature. However, electromagnetic noise and othersources of radiations related to the beam can create background. Since theSmith-Purcell radiation is linearly polarized, a way to decorrelate the signaland the background could then be to measure the two polarization components.The efficiency of the grating is given in Fig. 5 depending on the φ angle.This indicates that most of the radiation would be emitted along the x axisin a cone of approximately 40 ° opening, allowing all signal to enter the 100 mmoptics. Our simulations indicate that with the parameters used for our simulation alongitudinal bunch profile monitor based on Coherent Smith-Purcell radiationinstalled at near a high intensity proton beam would be sensitive to changesin the pulse length and could be useful in the tuning phase of such accelera-tor. However such device has never been tested at low β proton beams andpreliminary tests on a high intensity proton source would be useful. Acknowledgements E ne r g y pe r bun c h ( n J ) P1P2P1+P2
Fig. 4:
Simulation of the expected signal for a 3 ps bunch. P1 and P2 are thetwo polarization components.
The authors acknowledge George Doucas from John Adams Institute in Oxfordfor his useful advice.
References [1] A.V. Feschenko, PAC’01, Chicago, p. 517[2] S.Peggs (editor),
ESS Technical Design Report , (Lund, April 2013), chapter4, http://europeanspallationsource.se/documentation/tdr.pdf[3] G. Doucas, V. Blackmore, B. Ottewell, C. Perry, P. G. Huggard, E. Castro-Camus, M. B. Johnston, J. Lloyd Hughes, M. F. Kimmitt, B. Redlich, A.van der Meer, Phys. Rev. ST Accel. Beams 9, 092801 (2006)[4] J. H. Brownell, J. Walsh, G. Doucas, Phys. Rev. ST Accel. Beams 57, 1075(1998)[5] J. H. Brownell, G. Doucas, Phys. Rev. ST Accel. Beams 8, 092301 (2005)[6] H.L. Andrews et. al., Phys. Rev. ST Accel. Beams 17, 052802 (2014)[7] V. Blackmore, Ph.D. thesis, Oxford University, 2008
Acknowledgements Fig. 5:
Efficiency of the grating depending on the φ angle, for different θθ