A modified Thomson parabola spectrometer for high resolution multi-mev ion measurements - application to laser-driven ion acceleration D.C. Carroll a, P. McKenna a, P. Brummitt b, D. Neely b, F. Lindau c, O. Lundh c, C.-G. Wahlström c a SUPA, Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK b STFC, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK c Department 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 configuration is employed to enable a compact design capable of high resolution measurements of ion energy and charge-to-mass ratio. Practical issues relating to the use of the spectrometer for measurement of ion acceleration in high-power laser-plasma experiments are discussed. Example experimental results for 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 intensities that make it possible to generate beams of multi-mev ions [1 5] from laser-foil interactions. An important diagnostic for analyzing these ion beams is the Thomson parabola spectrometer [6 10]. This is used to measure the energy spectra of different ion species in a given solid angle. Magnetic and electric fields are used to deflect ions according to their velocity (v) and chargeto-mass ratio (q/m). It is a particularly useful diagnostic of laser-plasma interactions in which a range of ion species are accelerated. The most basic design for a Thomson parabola ion spectrometer involves the use of an electric field generated, by a potential difference across a pair of electrodes, and a magnetic field, generated by a pair of permanent magnets. These fields are parallel to each other but perpendicular to the ions initial direction of travel. The resulting ion dispersion, assuming uniform magnetic (B) and electric (E) fields, can be calculated using equations 1 and 2 for non-relativistic ions: D B = qbl ( ) B 1 mν z 2 L B + d B (1) D E = qel E mν 2 z ( ) 1 2 L E + d E (2) where D B and D E are the displacements due to the B and E fields, respectively, of an ion with charge q, mass m and velocity component, ν z, along the z-axis, being the initial ion direction. L E and L B are the lengths of the electric and magnetic fields along the z-axis. The distances between the end of the electric and magnetic fields and the detector plane are d E and d B, respectively. Equations 1 and 2 are the parametric equations of a parabola in terms of ν z, and hence ions with distinct q/m form parabolic traces in the dispersion plane of the spectrometer. The velocity spectrum is obtained from the density of ions along a given parabola. Ions with energies up to hundreds of MeV are produced in high power laser-plasma interactions [3, 11, 12]. To enable accurate identification of ion species with different q/m and accurate measurement of the maximum energy of these ions a spectrometer with a high charge-to-mass and energy resolution, in the MeV range, is required. One of the conditions to achieve this, is that a large and similar 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 in the direction orthogonal to the field. If permanent magnets are used then the field strength is defined by the magnet material and the pole separation. In principle, there is no limit to the dispersion that can be induced by this field as the particles will never intercept the magnets (though they could become trapped in circular orbits within the field). By contrast, as the E-field disperses ions in the direction of the field, the separation of the electrodes at the exit plane defines the energy range of the ions detected. In this paper we describe a modified Thomson parabola spectrometer, designed to produce high resolution measurements of the energy and charge states of multi-mev ions. The electromagnetic fields of this compact design are optimized to give greater dispersion for a given voltage compared to traditional designs and practical issues related to the use of the spectrometer are discussed. Example experimental results for multi-mev (up to 6 MeV per nucleon) highly charged (up to Au 42+ ) ion acceleration from high power laser interactions with thin foils, obtained using this spectrometer are presented. 2. Modified design To achieve the desired high charge-to-mass and energy resolution for ion acceleration driven by ultrahigh intensity lasers, while keeping the size of the spectrometer compact, a modified design of the Thomson ion spectrometer was developed as shown schematically in Fig. 1 and summarised in Table 1. The modified Thomson parabola spectrometer utilizes 50 mm 50 mm 10 mm permanent magnets with a pole separation of 20 mm to generate the B-field. NdFeB magnets give a peak field strength of 0.6 T at the central point between the magnets, while the same size ceramic magnets with the same pole separation generate a peak field of 0.2 T. The spectrometer is designed such that either field strength can be chosen by swapping magnets. The novel feature of the design is that it utilizes a wedge configuration for the E-field, in which the separation between the electrodes increases along the ion path. This 2 is designed to produce a large E-field dispersion and detectable energy range. To produce a similar dispersion to the magnetic field the electric field has to extend over a longer distance as the maximum potential which can be applied across the E-field electrodes is limited to 10 kv for practical consideration of compact power supplies. Figure 1: Schematic of the modified Thomson ion spectrometer. Ions are incident from the left, along the z-axis. Electrode length L E 200 mm Smallest electrode gap s min 2 mm Largest electrode gap s max 22.5 mm Magnet length L B 50 mm Magnet separation s B 20 mm Electrode to detector d E 45 mm Magnet to detector d B 195 mm Pinhole to detector d p 280 mm Table 1: Main parameters of the modified Thomson parabola spectrometer design. Fig. 2 shows the measured magnetic field variation along each of the three axes of the spectrometer. The peak magnetic field at the center of the gap between the two permanent magnets is measured to be 0.62 T (with NdFeB magnets). It should be noted that the Thomson spectrometers line of zero deflection, the path taken by neutral particles, is not along the center of the gap between the two magnets but is offset to the side by 3.5 mm so as to accommodate the tilted electrode configuration. The magnets are encased in a mild steel yoke to provide a return path for the field and so reduce fringe fields at the edges of the magnets. There is a slight asymmetry in the magnetic field due to variations in the thickness of the steel mounting; this can be seen in Fig. 2(b) and (c).
Figure 3: a) The coordinate system used for the mathematical description of the electric field. b) The calculated x-axis electric field component along the z-axis using the following typical values: V = 6000 V, θ0 = 0.1 rad (5.7 ), smin = 2 10 3 m, x = 1 10 3 m. Figure 2: a) The variation of the magnetic field across the gap between the two magnets. Measurements made inside the Thomson spectrometer 28 mm from the pinhole. b) Magnetic field 30 mm inside the spectrometer in the vertical plane parallel to the z-axis. c) Longitudinal scan of the magnetic field along the z-axis. The axes are defined in Fig. 1. The electric field (E) can be described at a given point between the electric plates in vector form [13], using the co-ordinate system defined in Fig. 3(a), as: zv Ex (x2 +z 2 )θ0 (3) 0 E (x, y, z > z0 ) = Ey = xv Ez (x2 +z 2 )θ0 where V is the voltage applied across the electrodes, θ0 is the angle between the plates and smin is the minimum separation of the plates. The electric field along the length of the Thomson parabola spectrometer, calculated using equation 3, with typical values for the spectrometer parameters, is shown in Fig. 3(b). It is assumed that outside the electrodes the electric field is zero. It should be noted that as the angle between the plates is small, the Ez component of the electric field is significantly smaller than the Ex component. A code has been developed to calculate the dispersion for ion species of interest, for the above measured magnetic and calculated electric fields. The total ion deflection due to the Lorentz force is calculated in incremental steps through the magnetic and electric fields along the z-axis. Fig. 4 shows the dispersion of proton and carbon ions as a function of energy in the range of interest, up to 60 MeV for protons and up to 5 MeV per nucleon for carbon ions, in the plane of the detector. Figure 4: The simulated dispersion of protons and carbon ions by the (a) magnetic and (b) electric fields at the plane of the detector. Only ions that avoid colliding with the electrodes and reach the detector plane are plotted. 3
Ion species with different q/m can be identified by comparing the measured shape of the parabolas at the detector plane to the calculated dispersion. After an ion species is identified by q/m dispersion, only one field is required to calculate the ion energy spectra. We typically us the B-field dispersion to extract the ion energy spectrum. Typical energy resolution with the B-field is E n /E n = 0.1 for E n = 60 MeV C 1+ ions over 100 µm, for the E-field this is E n /E n = 0.3. The limiting factor to the resolution (ignoring space charge effects) is the size of the pinhole used at the entrance of the spectrometer, as its projection at the detector plane defines the minimum separation required to resolve ions with different q/m and velocity. 3. Practical considerations The solid angle subtended by the entrance to the Thomson parabola spectrometer is selected depending on the flux of the ion beam and what information is to be extracted from the data. If an ion energy spectrum is required, for example to calculate the energy conversion efficiency from laser to ions, then a solid angle of 6 10 9 sr (equivalent to a 50 µm diameter pinhole at a distance of 0.6 m) is used to avoid saturation at low energies (few MeV) with a CR39 detector positioned as stated in Table 1. However, with this relatively small solid angle the maximum cut-off energy that can be resolved above background is reduced. If the maximum cut-off energy is required, then a solid angle of 2 10 8 sr (equivalent to a 100 µm diameter pinhole at 0.6 m) is found to be more suitable with a CR39 detector. The larger solid angle gives increased sensitivity at high energies which needs to be balanced with the resolution limiting effect of larger solid angle. Experience shows that a low pass R-C filter needs to be incorporated into the Thomson parabola spectrometer design due to the HV power cables connected to the spectrometer picking up high frequency noise in a petawatt laser-plasma environ- 4 ment. This noise is generated during the laser shots and causes instability in the E-field, which can result in unstable ion trajectories and steplike features at constant time in the ion trace at the detector plane. The modified Thomson parabola spectrometer described above has been used in a number of laser-foil ion acceleration experiments, involving laser intensities between 1 10 19 [14] and 6 10 20 Wcm 2 [15, 16]. The magnetic and electric field parameters of the Thomson parabola spectrometer can be modified to take account of the range of ion energies that are accelerated. The spectrometer as described above is for experiments using high energy, petawatt systems, e.g Vulcan (500 J in 500 fs) and the dispersion shown in Fig. 4 is optimized for this. On a multi-terawatt (1 J in 50 fs) laser system proton energies below 6 MeV [14] are typically measured. It is necessary for the strength of the fields in the Thomson parabola spectrometer to be reduced to optimize the dispersion for this lower energy range. Replacing the NdFeB magnets with same size but weaker ceramic magnets (to enable the same steel housing to be used) results in a magnetic field of 0.2 T. This together with the E-field dispersion generated by reducing the potential difference applied to 1.5 kv produces suitable dispersion. 4. Detectors Although CR39 (California Resin 39) is often used as the detector at the rear of the Thomson parabola spectrometer, other detectors can be used including scintillator with an EMCCD imaging system [14], micro-channel plate (MCP) [9, 10] and Fuji film image plate [17]. A 1 mm thick piece of CR-39 is sufficient to detect all heavy ions currently produced in laserfoil interactions and can detect protons with energy up to 11 MeV. Above this energy the protons pass straight through the CR-39. In comparison for deuterium and carbon ions to pass through 1 mm thick CR-39 requires energies > 15 MeV and > 250 MeV respectively. Ions are detected by etching the CR39 in a bath of heated sodium hydroxide solution (NaOH, e.g. 6.25 molar solution at 86 C) where damage caused to the plastic, due to ion energy deposition, develop into observable pits. A dynamic range for CR39 of about
two orders of magnitude in ion density is measurable. The limiting factor for the dynamic range is the pit density. If too high, the ion pits start to overlap and become difficult to identify individually, Fig. 5(a) shows an example of this. If too low, then distinguishing the signal from background can be an issue and statistical fluctuations are observable. The advantages of CR39 as an ion detector are that it is insensitive to electrons and photons, is 100% efficient and is not affected by electromagnetic pulses. The draw-backs of CR39 are that it is time consuming to process (multiple etching and analysis is required for ions stopped deep in the CR39) and is therefore ill-suited for a laser system with a high shot rate. Figure 5: a) Example ion parabola on CR39, insert A shows saturation of the CR39 where the scanner was unable to identify individual pits and insert B shows an expanded section of the parabola showing the high spatial resolution possible with the new Thomson spectrometer. b) Example spectra extracted from the raw CR39 data where the ion energy has been scaled with the ions atomic mass. Plastic scintillator detectors are sensitive to electrons and photons as well as ions. However, the response to electrons and photons is significantly reduced when using a thin (100 µm) scintillator while still being sensitive to ions. A dynamic range of about three orders is measurable with this detector when a 16-bit camera properly shielded is used. The advantage of using a scintillator imaging system is that it is an online diagnostic which can cope with a high rate of shots. The drawbacks are that it is not sensitive to individual ions like CR39 and therefore requires a higher ion flux to produce a measurable signal (a consequence of this is that a larger pinhole is required). Also, the thickness of the scintillator needs to be increased for increasing ion 5 energies, which in turn increases the background noise of electrons and photons. A similar system can be implemented where the scintillator is replaced 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 levels in the plate. The plate is then scanned in a purpose built scanner which de-excites these levels with a specific wavelength of light and causes light to be emitted that is read by the scanner. Once the plate is fully de-excited it can be reused. For image plate at the back of the Thomson parabola spectrometer the point of zero deflection is marked by x-rays passing along the unobstructed line-ofsight (for CR39 it is neutral atoms). The advantages of image plate are that it is quicker to process than CR39, it is reusable and can have a very large dynamic range [18, 19]. Its drawbacks are that it is not single-ion sensitive and it cannot be used as an online diagnostic. We have used all three types of detector. The image plate, scintillator and MCP can be absolutely calibrated either by using an ion beam whose parameters (energies and flux etc) are known or by cross referencing with CR39. 5. High resolution measurements of highly charged gold ions Fig. 5(a) shows an example digitized ion pit distribution on etched CR39. This is obtained with a 10 µm gold foil target is irradiated with the Vulcan Petawatt laser (Rutherford Appleton Laboratory) focused, with an f/3 off-axis parabola, to an intensity of 2.4 10 19 Wcm 2 at an incident angle of 45. The target is heated to 1000 C to remove water vapor and so preferentially accelerate heavier ions from the target foil [4, 20]. The modified Thomson spectrometer with a peak magnetic field of 0.62 T, a potential difference of 6 kv and a 1 mm thick piece of CR39 as detector is used to measure the accelerated ions. The solid angle of the spectrometer pinhole is 2 10 8 sr. The parabolas corresponding to different ion species are clearly seen. A zoomed in section of
the parabolas, Fig. 5(a) insert B, shows the clearly separated Au charge states. The multiply charged C q+ and Au q+ up to q = 5 and q = 42, respectively, are clearly resolved. Example spectra of both carbon and gold ions are shown in Fig. 5(b). In this example the highest energy ions are found to be the highest charge states, 0.6 MeV/nucleon for Au 42+ (118 MeV)and 6 MeV/nucleon for C 5+ (72 MeV). [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. summary We have presented a modified Thomson parabola spectrometer design to enable high resolution measurements of many-charge state multi-mev ion emission. In addition this spectrometer design is compact and versatile with interchangeable magnets. Example experimental measurements of individually resolved tracks of Au q+ ions up to q = 42 are presented. Thomson spectrometers of this design have been used in a variety of experiments [14 16, 21] on both high power single shot and high shot rate laser systems. 7. Acknowledgments We acknowledge expert support of the staff at the Central Laser Facility. This work was supported by the UK Engineering and Physical Sciences Research Council (grant numbers EP/E048668/1 and 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. Mróz 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). 6