A modified Thomson parabola spectrometer for high resolution multi-MeV

ion measurements - application to laser-driven ion acceleration

D.C. Carrolla, P. McKennaa, P. Brummittb, D. Neelyb, F. Lindauc, O. Lundhc, C.-G. Wahlstromc

aSUPA, Department of Physics, University of Strathclyde, Glasgow G4 0NG, UKbSTFC, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UKcDepartment of Physics, Lund University, P.O. Box 118, 221 00 Lund, Sweden

Abstract

A novel Thomson parabola ion spectrometer design is presented, in which a gradient electric field con-figuration is employed to enable a compact design capable of high resolution measurements of ion energyand charge-to-mass ratio. Practical issues relating to the use of the spectrometer for measurement ofion acceleration in high-power laser-plasma experiments are discussed. Example experimental resultsfor ion acceleration from petawatt-class laser interactions with thin gold target foils are presented.

Key words:

1. Introduction

In recent years, laser systems have reached in-tensities that make it possible to generate beamsof multi-MeV ions [1–5] from laser-foil interac-tions. An important diagnostic for analyzing theseion beams is the Thomson parabola spectrometer[6–10]. This is used to measure the energy spec-tra of different ion species in a given solid angle.Magnetic and electric fields are used to deflections according to their velocity (v) and charge-to-mass ratio (q/m). It is a particularly usefuldiagnostic of laser-plasma interactions in which arange of ion species are accelerated. The mostbasic design for a Thomson parabola ion spec-trometer involves the use of an electric field gen-erated, by a potential difference across a pair ofelectrodes, and a magnetic field, generated by apair of permanent magnets. These fields are par-allel to each other but perpendicular to the ions’initial direction of travel. The resulting ion dis-persion, assuming uniform magnetic (B) and elec-tric (E) fields, can be calculated using equations1 and 2 for non-relativistic ions:

DB =qBLBmνz

(1

2LB + dB

)(1)

DE =qELEmν2

z

(1

2LE + dE

)(2)

where DB and DE are the displacements due tothe B and E fields, respectively, of an ion withcharge q, mass m and velocity component, νz,along the z-axis, being the initial ion direction.LE and LB are the lengths of the electric andmagnetic fields along the z-axis. The distances be-tween the end of the electric and magnetic fieldsand the detector plane are dE and dB, respec-tively. Equations 1 and 2 are the parametric equa-tions of a parabola in terms of νz, and hence ionswith distinct q/m form parabolic traces in thedispersion plane of the spectrometer. The veloc-ity spectrum is obtained from the density of ionsalong a given parabola.

Ions with energies up to hundreds of MeV areproduced in high power laser-plasma interactions[3, 11, 12]. To enable accurate identification of ionspecies with different q/m and accurate measure-ment of the maximum energy of these ions a spec-trometer with a high charge-to-mass and energyresolution, in the MeV range, is required. One ofthe conditions to achieve this, is that a large andsimilar dispersion is induced by both the B and

Preprint submitted to Nuclear Instruments and Methods in Physics Research Section A November 5, 2009

E-fields. The dispersion due to the B-field is inthe direction orthogonal to the field. If perma-nent magnets are used then the field strength isdefined by the magnet material and the pole sepa-ration. In principle, there is no limit to the disper-sion that can be induced by this field as the parti-cles will never intercept the magnets (though theycould become trapped in circular orbits withinthe field). By contrast, as the E-field dispersesions in the direction of the field, the separation ofthe electrodes at the exit plane defines the energyrange of the ions detected.

In this paper we describe a modified Thomsonparabola spectrometer, designed to produce highresolution measurements of the energy and chargestates of multi-MeV ions. The electromagneticfields of this compact design are optimized to givegreater dispersion for a given voltage compared totraditional designs and practical issues related tothe use of the spectrometer are discussed. Exam-ple experimental results for multi-MeV (up to 6MeV per nucleon) highly charged (up to Au42+)ion acceleration from high power laser interactionswith thin foils, obtained using this spectrometerare presented.

2. Modified design

To achieve the desired high charge-to-mass andenergy resolution for ion acceleration driven by ul-trahigh intensity lasers, while keeping the size ofthe spectrometer compact, a modified design ofthe Thomson ion spectrometer was developed asshown schematically in Fig. 1 and summarised inTable 1. The modified Thomson parabola spec-trometer utilizes 50 mm × 50 mm × 10 mm per-manent magnets with a pole separation of 20 mmto generate the B-field. NdFeB magnets give apeak field strength of ∼0.6 T at the central pointbetween the magnets, while the same size ceramicmagnets with the same pole separation generatea peak field of ∼0.2 T. The spectrometer is de-signed such that either field strength can be cho-sen by swapping magnets. The novel feature ofthe design is that it utilizes a wedge configurationfor the E-field, in which the separation betweenthe electrodes increases along the ion path. This

is designed to produce a large E-field dispersionand detectable energy range. To produce a similardispersion to the magnetic field the electric fieldhas to extend over a longer distance as the max-imum potential which can be applied across theE-field electrodes is limited to ∼ 10 kV for prac-tical consideration of compact power supplies.

Figure 1: Schematic of the modified Thomson ion spec-trometer. Ions are incident from the left, along the z-axis.

Electrode length LE 200 mmSmallest electrode gap smin 2 mmLargest electrode gap smax 22.5 mmMagnet length LB 50 mmMagnet separation sB 20 mmElectrode to detector dE 45 mmMagnet to detector dB 195 mmPinhole to detector dp 280 mm

Table 1: Main parameters of the modified Thomsonparabola spectrometer design.

Fig. 2 shows the measured magnetic field vari-ation along each of the three axes of the spec-trometer. The peak magnetic field at the centerof the gap between the two permanent magnets ismeasured to be 0.62 T (with NdFeB magnets). Itshould be noted that the Thomson spectrometersline of zero deflection, the path taken by neutralparticles, is not along the center of the gap be-tween the two magnets but is offset to the sideby 3.5 mm so as to accommodate the tilted elec-trode configuration. The magnets are encased ina mild steel yoke to provide a return path for thefield and so reduce fringe fields at the edges of themagnets. There is a slight asymmetry in the mag-netic field due to variations in the thickness of thesteel mounting; this can be seen in Fig. 2(b) and(c).

2

Figure 2: a) The variation of the magnetic field acrossthe gap between the two magnets. Measurements madeinside the Thomson spectrometer 28 mm from the pinhole.b) Magnetic field 30 mm inside the spectrometer in thevertical plane parallel to the z-axis. c) Longitudinal scanof the magnetic field along the z-axis. The axes are definedin Fig. 1.

The electric field (E) can be described at agiven point between the electric plates in vectorform [13], using the co-ordinate system defined inFig. 3(a), as:

E (x, y, z > z0) =

ExEyEz

=

zV(x2+z2)θ0

0−xV

(x2+z2)θ0

(3)

where V is the voltage applied across the elec-trodes, θ0 is the angle between the plates and sminis the minimum separation of the plates. Theelectric field along the length of the Thomsonparabola spectrometer, calculated using equation3, with typical values for the spectrometer param-eters, is shown in Fig. 3(b).

It is assumed that outside the electrodes theelectric field is zero. It should be noted that as

Figure 3: a) The coordinate system used for the mathe-matical description of the electric field. b) The calculatedx-axis electric field component along the z-axis using thefollowing typical values: V = 6000 V, θ0 = 0.1 rad (5.7◦),smin = 2× 10−3 m, x = 1× 10−3 m.

the angle between the plates is small, the Ez com-ponent of the electric field is significantly smallerthan the Ex component.

A code has been developed to calculate thedispersion for ion species of interest, for the abovemeasured magnetic and calculated electric fields.The total ion deflection due to the Lorentz force iscalculated in incremental steps through the mag-netic and electric fields along the z-axis. Fig. 4shows the dispersion of proton and carbon ions asa function of energy in the range of interest, up to60 MeV for protons and up to 5 MeV per nucleonfor carbon ions, in the plane of the detector.

Figure 4: The simulated dispersion of protons and carbonions by the (a) magnetic and (b) electric fields at the planeof the detector. Only ions that avoid colliding with theelectrodes and reach the detector plane are plotted.

3

Ion species with different q/m can be iden-tified by comparing the measured shape of theparabolas at the detector plane to the calculateddispersion. After an ion species is identified byq/m dispersion, only one field is required to cal-culate the ion energy spectra. We typically us theB-field dispersion to extract the ion energy spec-trum. Typical energy resolution with the B-fieldis ∆En/En = 0.1 for En = 60 MeV C1+ ions over100 µm, for the E-field this is ∆En/En = 0.3 .

The limiting factor to the resolution (ignoringspace charge effects) is the size of the pinhole usedat the entrance of the spectrometer, as its projec-tion at the detector plane defines the minimumseparation required to resolve ions with differentq/m and velocity.

3. Practical considerations

The solid angle subtended by the entrance tothe Thomson parabola spectrometer is selecteddepending on the flux of the ion beam and whatinformation is to be extracted from the data. Ifan ion energy spectrum is required, for exampleto calculate the energy conversion efficiency fromlaser to ions, then a solid angle of ∼ 6 × 10−9 sr(equivalent to a 50 µm diameter pinhole at a dis-tance of 0.6 m) is used to avoid saturation at lowenergies (few MeV) with a CR39 detector posi-tioned as stated in Table 1. However, with thisrelatively small solid angle the maximum cut-offenergy that can be resolved above background isreduced. If the maximum cut-off energy is re-quired, then a solid angle of ∼ 2× 10−8 sr (equiv-alent to a 100 µm diameter pinhole at 0.6 m) isfound to be more suitable with a CR39 detector.The larger solid angle gives increased sensitivityat high energies which needs to be balanced withthe resolution limiting effect of larger solid angle.

Experience shows that a low pass R-C filterneeds to be incorporated into the Thomson parabolaspectrometer design due to the HV power cablesconnected to the spectrometer picking up high fre-quency noise in a petawatt laser-plasma environ-ment. This noise is generated during the lasershots and causes instability in the E-field, whichcan result in unstable ion trajectories and step-

like features at constant time in the ion trace atthe detector plane.

The modified Thomson parabola spectrome-ter described above has been used in a number oflaser-foil ion acceleration experiments, involvinglaser intensities between 1×1019 [14] and 6×1020

Wcm−2 [15, 16]. The magnetic and electric fieldparameters of the Thomson parabola spectrome-ter can be modified to take account of the range ofion energies that are accelerated. The spectrom-eter as described above is for experiments usinghigh energy, petawatt systems, e.g Vulcan (500 Jin 500 fs) and the dispersion shown in Fig. 4 isoptimized for this. On a multi-terawatt (1 J in 50fs) laser system proton energies below 6 MeV [14]are typically measured. It is necessary for thestrength of the fields in the Thomson parabolaspectrometer to be reduced to optimize the dis-persion for this lower energy range. Replacingthe NdFeB magnets with same size but weakerceramic magnets (to enable the same steel hous-ing to be used) results in a magnetic field of ∼ 0.2T. This together with the E-field dispersion gener-ated by reducing the potential difference appliedto 1.5 kV produces suitable dispersion.

4. Detectors

Although CR39 (California Resin 39) is oftenused as the detector at the rear of the Thom-son parabola spectrometer, other detectors can beused including scintillator with an EMCCD imag-ing system [14], micro-channel plate (MCP) [9, 10]and Fuji film image plate [17].

A 1 mm thick piece of CR-39 is sufficient todetect all heavy ions currently produced in laser-foil interactions and can detect protons with en-ergy up to 11 MeV. Above this energy the protonspass straight through the CR-39. In comparisonfor deuterium and carbon ions to pass through1 mm thick CR-39 requires energies > 15 MeVand > 250 MeV respectively. Ions are detectedby etching the CR39 in a bath of heated sodiumhydroxide solution (NaOH, e.g. 6.25 molar solu-tion at 86◦C) where damage caused to the plastic,due to ion energy deposition, develop into observ-able pits. A dynamic range for CR39 of about

4

two orders of magnitude in ion density is measur-able. The limiting factor for the dynamic rangeis the pit density. If too high, the ion pits startto overlap and become difficult to identify indi-vidually, Fig. 5(a) shows an example of this. Iftoo low, then distinguishing the signal from back-ground can be an issue and statistical fluctuationsare observable. The advantages of CR39 as an iondetector are that it is insensitive to electrons andphotons, is 100% efficient and is not affected byelectromagnetic pulses. The draw-backs of CR39are that it is time consuming to process (multipleetching and analysis is required for ions stoppeddeep in the CR39) and is therefore ill-suited for alaser system with a high shot rate.

Figure 5: a) Example ion parabola on CR39, insert Ashows saturation of the CR39 where the scanner was un-able to identify individual pits and insert B shows an ex-panded section of the parabola showing the high spatialresolution possible with the new Thomson spectrometer.b) Example spectra extracted from the raw CR39 datawhere the ion energy has been scaled with the ions atomicmass.

Plastic scintillator detectors are sensitive toelectrons and photons as well as ions. However,the response to electrons and photons is signifi-cantly reduced when using a thin (100 µm) scin-tillator while still being sensitive to ions. A dy-namic range of about three orders is measurablewith this detector when a 16-bit camera prop-erly shielded is used. The advantage of using ascintillator imaging system is that it is an on-line diagnostic which can cope with a high rateof shots. The drawbacks are that it is not sen-sitive to individual ions like CR39 and thereforerequires a higher ion flux to produce a measurablesignal (a consequence of this is that a larger pin-hole is required). Also, the thickness of the scin-tillator needs to be increased for increasing ion

energies, which in turn increases the backgroundnoise of electrons and photons. A similar systemcan be implemented where the scintillator is re-placed with a MCP and phosphor screen.

Fuji film image plate (Fuji Photo Film Co.Ltd) is a reusable film where ionizing radiation(ions, electrons and photons) excite electron lev-els in the plate. The plate is then scanned in apurpose built scanner which de-excites these levelswith a specific wavelength of light and causes lightto be emitted that is read by the scanner. Oncethe plate is fully de-excited it can be reused. Forimage plate at the back of the Thomson parabolaspectrometer the point of zero deflection is markedby x-rays passing along the unobstructed line-of-sight (for CR39 it is neutral atoms). The advan-tages of image plate are that it is quicker to pro-cess than CR39, it is reusable and can have a verylarge dynamic range [18, 19]. Its drawbacks arethat it is not single-ion sensitive and it cannot beused as an online diagnostic.

We have used all three types of detector. Theimage plate, scintillator and MCP can be abso-lutely calibrated either by using an ion beam whoseparameters (energies and flux etc) are known orby cross referencing with CR39.

5. High resolution measurements of highlycharged gold ions

Fig. 5(a) shows an example digitized ion pitdistribution on etched CR39. This is obtainedwith a 10 µm gold foil target is irradiated with theVulcan Petawatt laser (Rutherford Appleton Lab-oratory) focused, with an f/3 off-axis parabola, toan intensity of 2.4 × 1019 Wcm−2 at an incidentangle of 45◦. The target is heated to 1000 ◦C toremove water vapor and so preferentially acceler-ate heavier ions from the target foil [4, 20].

The modified Thomson spectrometer with apeak magnetic field of 0.62 T, a potential differ-ence of 6 kV and a 1 mm thick piece of CR39as detector is used to measure the acceleratedions. The solid angle of the spectrometer pinholeis ∼ 2× 10−8 sr.

The parabolas corresponding to different ionspecies are clearly seen. A zoomed in section of

5

the parabolas, Fig. 5(a) insert B, shows the clearlyseparated Au charge states. The multiply chargedCq+ and Auq+ up to q = 5 and q = 42, respec-tively, are clearly resolved. Example spectra ofboth carbon and gold ions are shown in Fig. 5(b).In this example the highest energy ions are foundto be the highest charge states, 0.6 MeV/nucleonfor Au42+ (118 MeV)and 6 MeV/nucleon for C5+

(72 MeV).

6. summary

We have presented a modified Thomson parabolaspectrometer design to enable high resolution mea-surements of many-charge state multi-MeV ionemission. In addition this spectrometer design iscompact and versatile with interchangeable mag-nets. Example experimental measurements of in-dividually resolved tracks of Auq+ ions up to q =42 are presented. Thomson spectrometers of thisdesign have been used in a variety of experiments[14–16, 21] on both high power single shot andhigh shot rate laser systems.

7. Acknowledgments

We acknowledge expert support of the staff atthe Central Laser Facility. This work was sup-ported by the UK Engineering and Physical Sci-ences Research Council (grant numbers EP/E048668/1and EP/E035728/1) and the LIBRA consortium.

References

[1] E. L. Clark et al., Phys. Rev. Lett. 84, 670 (2000).[2] E. L. Clark et al., Phys. Rev. Lett. 85, 1654 (2000).[3] R. A. Snavely et al., Phys. Rev. Lett. 85, 2945 (2000)[4] M. Hegelich et al., Phys. Rev. Lett. 89, 085002

(2002).[5] M. Borghesi et al., Fusion Sci. Techn. 49, 412 (2006).[6] 1. S. Sakabe et al., Rev. Sci. Instr. 51, 1314 (1980).[7] M. J. Rhee et al., Rev. Sci. Instr. 58, 240 (1987).[8] Ming-fang Lu et al., Rev. Sci. Instr. 68, 3738 (1997).[9] W. Mroz et al., Rev. Sci. Instr. 71, 1417 (2000).

[10] K. Harres et al., Rev. Sci. Instr. 79, 093306 (2008).[11] L. Robson et al., Nat. Phys. 3, 58 (2007).[12] A. Henig et al., Phys. Rev. Lett. 103, 045002 (2009).[13] K.-I. Sakai et al., IEEE Trans. Diele. Elect. Insul. 10,

404 (2003).[14] A. P. L. Robinson et al., New J. Phys. 11, 083018

(2009).

[15] P. McKenna et al., Phys. Rev. Lett. 98, 145001(2007).

[16] P. McKenna et al., Plasma Phys. Controll. Fusion 49,B223 (2007).

[17] www.fujifilm.com[18] R.J. Clarke et al., Nucl. Instr. Meth. Phys. Res. A

585, 117 (2008).[19] T. Tanimoto et al., Rev. Sci. Instr. 79, 10E910 (2008).[20] P. McKenna et al., Phys. Rev. E 70, 036405 (2004).[21] A. S. Pirozhkov et al., App. Phys. Lett. 94, 241102

(2009).

6