Proton deflectometry of a capacitor coil target along two axes Download: 524次
1 Introduction
Capacitor coils are a type of laser-driven solenoid that consists of two metal plates held in parallel, connected by a loop of wire or metallic ribbon[1–3]. A high-energy laser beam is used to accelerate hot electrons[4, 5] from the rear plate (anode) onto the front plate (cathode)[6]. A return current is then established along the connecting loop, generating a quasi-static magnetic field that can be used in high energy density physics experiments[2, 7, 8]. There are numerous potential applications of uniform magnetic fields exceeding
Capacitor coil magnetic fields of 1–1000 T have been reported at different laser facilities using a range of diagnostics, although harsh laser-plasma conditions make it difficult to reliably estimate the magnetic field inside the coil loop[1–3, 8, 16–19]. High-frequency B-dot probes can measure the full time evolution of a capacitor coil magnetic field, but are highly sensitive to electromagnetic pulse noise[20, 21] and must be positioned several centimetres from the target to avoid radiation damage. This introduces significant errors in the signal analysis because the magnetic field geometry must be simulated and extrapolated over a long distance. These simulations also require the target current geometry to be known accurately, which is difficult in a complex, closed geometry that combines an expanding plate plasma with photoionization effects[22]. Faraday rotation has been used as a localized magnetic field diagnostic, but the birefringent crystals responsible for polarization of the probe beam must be shielded from plasma X-rays to avoid crystal blanking[16]. This is challenging in a millimetre-scale loop where shorting of the capacitor must be avoided. In light of these limitations, proton deflectometry is frequently used to corroborate inductive and magneto-optic measurements[16, 19].
Proton deflectometry with radiochromic film[23] (RCF) is an ideal diagnostic of capacitor coil experiments because it can produce multi-dimensional images of electromagnetic fields with micron spatial and picosecond temporal resolution[24–26]. When a proton beam passes across a capacitor coil target, the proton trajectories are modified by strong electric and magnetic fields; these protons then propagate through space until they strike a stack of RCF, where they deposit their energy in different layers of film according to their Bragg curve[24]. The protons in our experiment were generated by the target normal sheath acceleration (TNSA) mechanism[27]. TNSA-generated proton beams have a broad spectral range and probe the target at different times corresponding to the proton time of flight from source to target. Previous capacitor coil experiments have focused on proton deflectometry perpendicular to the loop axis[16, 17], where protons on one side of the loop are deflected radially outwards and protons on the opposite side are pinched radially inwards by the poloidal magnetic field. These experiments produce a distinctive teardrop-shaped proton void, with a width proportional to the square root of the loop current[17]. It is difficult to extract a definitive measurement of the magnetic field because the void width is also affected by electric fields in the target[8, 28]. Breaking the degeneracy of the electric and magnetic fields is essential when assessing the suitability of capacitor coil targets for magnetized high energy density experiments. To reliably quantify the magnetic field strength in a capacitor coil target, we require monoenergetic proton images of the loop at different energies or proton probing from multiple directions.
In this paper, we present proton probing of a capacitor coil target along two axes. Figure
Fig. 1. Left: Sample proton radiograph taken perpendicularly to the axis of a 2-mm-diameter wire loop with $E_{p}=7.3\pm 0.05~\text{MeV}$ protons. The void width, $w$ , is proportional to the square root of the current flowing in the coil loop[17], though $w$ is also affected by electric fields. Right: Sample proton radiograph taken parallel to the axis of a 1-mm-diameter wire loop with $E_{p}=6.5\pm 0.07~\text{MeV}$ protons. Notice how the outline of an Au grid has been imprinted in the proton beam as a fiducial. Each RCF image has a magnification of $M=10$ , so a distance of 5 mm in the detector plane (indicated above) equates to 0.5 mm in the coil plane.
Since proton deflection in electromagnetic fields depends on the proton energy,
Proton deflectometry has been used in single- and dual-axis configurations to diagnose magnetic fields in laser-heated plasmas[29, 30] and pulsed power discharges[31, 32]. Of these different methods, comparing simultaneous dual-axis images has the clear advantage that it allows one to examine E/B-fields under identical conditions from two directions[30]. This is particularly useful if the field geometry is asymmetrical or if there is significant shot-to-shot variation in the laser parameters. We will present our parallel and perpendicular data separately. We found it was not necessary to compare the two axes simultaneously for relatively low wire currents (
All data used to produce the figures in this work, along with other supporting materials, can be found at http://dx.doi.org/10.15124/79ca0a38-dddb-480c-9edf-d8f52496dfad.
2 Experimental setup
Our experiment was conducted on the Vulcan Target Area West (TAW) laser system at the Central Laser Facility. Three ‘long pulse’ beams were used to drive the capacitor coil with a combined energy of
Fig. 2. Photograph of full capacitor coil target assembly with two proton foils and Au grids. Two rectangular Au foils of $40~\unicode[STIX]{x03BC}\text{m}$ thickness with $5~\unicode[STIX]{x03BC}\text{m}$ Au shields were used for TNSA proton radiography. Between the proton foils and the capacitor coil, two Au grids were installed to act as visual references in the proton images. RCF stacks were positioned 10 cm behind the target to detect the protons along two axes.
3 Proton deflectometry
3.1 Synthetic proton deflectometry
By comparing the experimental RCF data to synthetic proton radiographs generated using the EPOCH particle-in-cell code[34], it is possible to estimate the loop current and corresponding magnetic flux density inside a capacitor coil target. Static magnetic fields were calculated for an arbitrary current geometry using a Python finite difference code. These fields were then imported into EPOCH, where a monoenergetic, divergent beam of protons was propagated through the simulation box. Simulations were run on a cubic Cartesian grid, 6 mm wide, with four particles per cell and a grid separation of
3.2 Perpendicular deflectometry: B-field-only simulations
Simulated radiographs of protons passing perpendicularly across a static capacitor coil magnetic field are shown in Figure
Fig. 3. Comparison of EPOCH simulations with RCF data for (a) 1-mm- and (b) 2-mm-diameter capacitor coil loops. EPOCH simulations used a monoenergetic $E_{p}=7~\text{MeV}$ proton beam with a divergence angle of $40^{\circ }$ . The RCF data shown corresponds to protons with energy $E_{p}=7.3\pm 0.05~\text{MeV}$ . Proton voids are bigger at early times ($t\sim 0.3~\text{ns}$ ) before decaying to a stable value for $t>0.8~\text{ns}$ . Estimated loop currents at $t>0.8~\text{ns}$ are $J=5~\text{kA}$ for both loop diameters. The magnification of each RCF image is $M=10$ , so a distance of 5 mm in the detector plane (indicated above) equates to 0.5 mm in the coil plane.
Fig. 4. Left: Experimental RCF data for a 1-mm-diameter loop taken at $t\sim 0.8~\text{ns}$ with $E_{p}=7.3\pm 0.05~\text{MeV}$ protons. Right: Synthetic proton radiograph for 7 MeV protons passing across a 1-mm-diameter loop with capacitor-coil-shaped B-field and a uniformly charged circular ring. Note that the loop current that best matches the RCF data is now three times higher than that in Figure 3 ($J=15~\text{kA}$ versus $J=5~\text{kA}$ ). Horizontal and vertical lines are provided as fiducials. The magnification of each RCF image is $M=10$ , so a distance of 5 mm in the detector plane (indicated above) equates to 0.5 mm in the coil plane.
Fig. 5. Demonstration of the effect of positive wire electric fields on proton void structure. In these deflectometry simulations, 7 MeV protons were propagated perpendicularly across a 1-mm-diameter wire loop. Horizontal and vertical lines have been cut out of the proton distribution to act as fiducials. Left: Simulation run with electric fields only. Electric fields were calculated for a uniformly charged wire loop with total charge $Q=10~\text{nC}$ . Proton displacement is approximately constant across the entire length of the wire. Distortion of the fiducial grid is only observed near the top of the loop – not near the vertical wire sections. Right: Simulation run with electric and magnetic fields. Electric fields were calculated for a uniformly charged wire loop with total charge $Q=5~\text{nC}$ , while magnetic fields were generated from a uniform wire current of $J=5~\text{kA}$ . The proton void width is 6 mm – approximately 1 mm larger than that observed for the same simulation without an electric field.
Fig. 6. (a) Axial proton radiograph for a 2-mm-diameter loop, $t\sim 0.8~\text{ns}$ after the beginning of the laser drive. Image taken using $E_{p}=7.3\pm 0.05~\text{MeV}$ protons. Two areas have been highlighted with white circles: Region 1, axial proton void at the centre of the capacitor coil loop; Region 2, grid distortion is concentrated at the base of the vertical wires and around the plates. (b) Synthetic proton radiograph for a circular ring of current ($J=40~\text{kA}$ ) with an overlapped circular ring of charge ($Q=-80~\text{nC}$ ). (c) Synthetic proton radiograph for a capacitor coil wire carrying $J=40~\text{kA}$ with an overlapped uniform charge distribution ($Q=-110~\text{nC}$ ). Each RCF image is magnified by a factor $M=10$ , so a distance of 5 mm in the detector plane (indicated above) equates to 0.5 mm in the coil plane. Insets in the bottom right hand corner of (b) and (c) are diagrams of the conductor geometry used in each simulation.
3.3 Perpendicular deflectometry: combined E- and B-field simulations
An accumulation of negative charge in the vicinity of the wire loop could produce strong electric fields that reduce the size of the proton void generated by the magnetic fields. Thus simulations that include negative electric charges can predict higher loop currents than simulations with just a magnetic field alone[8]. A spherical charge distribution placed near the wire loop and Cu plates produced unrepresentative synthetic radiographs, so we have chosen to study two alternative charge geometries: a circular ring and a capacitor coil loop. In Figure
Charge separation in the laser focal spot will generate a positive potential that spreads out over the capacitor coil plates and connecting wire[21, 28, 35, 36]. A positively charged wire acts to deflect protons radially away from the wire surface. These protons are deflected outwards by a similar amount all along the wire, so positive electric fields cannot reproduce a teardrop-shaped void without magnetic fields. Electric fields can, however, increase the width of the proton void generated by a magnetic field as well as the apparent thickness of the vertical wire sections (see Figure
The larger the electrostatic charge, the stronger the grid deflection around the loop. In Section
3.4 Axial deflectometry: negative charge distribution
Grid deflection in the axial proton images can provide information about the likely charge distribution present around the target – essential for accurate simulations of proton deflectometry. Figure
In Figure
Fig. 7. Synthetic proton radiographs for a 1-mm-diameter charged ring on top of a capacitor coil loop carrying a current $J=15~\text{kA}$ . Vertical and horizontal lines have been cut out of the proton beam to act as fiducials. (a) Grid deflection is minimal around the loop for B-field simulations with a static current. (b) For $Q=-10~\text{nC}$ , we see millimetre-scale grid deflections consistent with the RCF data. (c) For $Q=-40~\text{nC}$ , grid deflection is of centimetre scale and much larger than that observed on the RCF.
3.5 Axial deflectometry: upper limits on capacitor coil magnetic field
EPOCH simulations of protons passing through a current loop suggest that the beam will rotate as it passes through the magnetic field (clockwise or anticlockwise depending on the polarization of the current). Thus if a fiducial (e.g., high-
Fig. 8. (a) Synthetic radiograph for a 7 MeV divergent proton beam passing through the magnetic field of a 2-mm-diameter current loop carrying a current $J=100~\text{kA}$ . A vertical slot is cut out of the Gaussian proton distribution, which rotates through an approximately fixed $13^{\circ }$ angle inside the loop. (b) Blue points: graph of loop current plotted against rotation angle of the fiducial grid for a 2-mm-diameter current loop. Since there is no evidence of grid rotation in the RCF data, this puts an upper limit on the loop current of less than $J=10~\text{kA}$ . The straight line represents proton gyration angle for protons passing perpendicularly through a uniform magnetic field of 1 mm spatial scale. The magnitude of this magnetic field is equivalent to the B-field at the centre of a 2-mm-diameter current loop.
Fig. 9. (a) Study of grid rotation with different loop charges. Negative charge is distributed uniformly along the capacitor coil loop and the proton beam divergence angle is fixed at $40^{\circ }$ . We can see that the angle of rotation of the grid is unchanged for different loop charges. (b) Proton beam with zero divergence passing through the magnetic field of a current loop carrying $J=40~\text{kA}$ – the grid rotation angle is unchanged versus the $40^{\circ }$ case.
Grid deflection close to the wire surface can also be used as a measure of the wire current and magnetic field. The vertical wires under the capacitor coil loop provide a simplified geometry for conducting simulations of the magnetic field. Figure
Fig. 10. (a) Magnetic field geometry used in simulations of two vertical wires with opposite currents. (b) Synthetic radiograph for two vertical wires carrying $J=\pm 20~\text{kA}$ . Horizontal fiducial demonstrates multi-millimetre grid deflection close to the wire surface. Approximate location of the wire surface is picked out with vertical dashed lines. (c) Detail from RCF image of 1-mm-diameter loop taken $t\sim 0.8~\text{ns}$ after the beginning of the laser drive. Though there is no clear evidence of a continuous grid deflection around the vertical wires, a smeared-out region ${\sim}1{-}2~\text{mm}$ thick around the wire puts an upper limit on the wire current at $J\sim 5~\text{kA}$ .
4 Discussion
Comparing synthetic proton radiographs with a range of current and charge distributions is necessary to place upper and lower limits on the capacitor coil magnetic field. EPOCH simulations show that negative charges around the wire allow us to infer larger loop currents, but there is no experimental evidence for this effect in the axial RCF data. Enhanced current estimates of
The approximate magnetic field energy for the 1-mm-diameter targets is given by
The hot electron temperature achieved in the laser focal spot can be estimated from the Forslund
Based on a laser-diode model of the capacitor coil target[6], for a hot electron temperature of
5 Conclusion
In summary, we have demonstrated dual-axis proton probing of the electromagnetic fields around a capacitor coil target at a laser drive intensity of
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Article Outline
P. Bradford, M. P. Read, M. Ehret, L. Antonelli, M. Khan, N. Booth, K. Glize, D. Carroll, R. J. Clarke, R. Heathcote, S. Ryazantsev, S. Pikuz, C. Spindloe, J. D. Moody, B. B. Pollock, V. T. Tikhonchuk, C. P. Ridgers, J. J. Santos, N. C. Woolsey. Proton deflectometry of a capacitor coil target along two axes[J]. High Power Laser Science and Engineering, 2020, 8(2): 02000e11.