Scaled beam merging experiment for heavy ion inertial fusion

Transverse beam combining is a cost-saving option employed in many designs for heavy ion fusion drivers. However, the resultant transverse phase space dilution must be minimized so as not to sacrifice focusability at the target. A prototype combining experiment has been completed employing four 3-mA ${\mathrm{Cs}}^{+}$ beams injected at 160 keV. The focusing elements upstream of the merge consist of four quadrupoles and a final combined-function element (quadrupole and dipole). Following the merge, the resultant single beam is transported in a single alternating gradient channel where the subsequent evolution of the distribution function is diagnosed. The results are in fair agreement with particle-in-cell simulations. They indicate that for some heavy ion fusion driver designs, the phase space dilution from merging is acceptable.

Figure 1

A CAD view of the lattice elements of the Combiner apparatus. Diagnostics are at locations marked $d1$ and $d2$. The first four elements ($Q1–Q4$) are electrostatic quadrupoles. Each of the quadrupoles of $Q2$ is separately moveable in both horizontal and vertical dimensions. $QD5$ is the combined function dipole and quadrupole, for which the electrostatic field-defining rods around each beam converge as $z$ increases. The distance from the source emitting surfaces to the end of $QD5$ is $\approx 108\mathrm{cm}$.

Figure 2

(a) Schematic of the beam footprints at the exit of $QD5$. The individual beam semimajor and semiminor axes are 6.5 and 3.7 mm. The beam edge to beam-edge clearance is $\Delta =4\mathrm{mm}$. The upstream matching solution is chosen so that the beam envelope divergence angles are zero ($a^{\prime }=b^{\prime }=0$) at this point, which also helps to minimize phase space dilution of the merged beam. (b) The dipole component is apparent from the equipotentials (calculated in a 2D approximation) of the merge element due to the voltages on the rods of $QD5$.

Figure 3

Transverse beam profiles measured at the $d1$ diagnostic station. The rms beam radii are identical to within $\pm 0.2\mathrm{mm}$.

Figure 4

Measured transverse phase space at $d2$ of one beam compared to the result from PIC simulations. The contour lines indicate 10% increments in relative intensity, and the color code sequence from lowest to highest intensity is blue, …, red.

Figure 5

Horizontal phase space measurement (bottom panel) versus PIC simulation (top panel) at the $d3$ diagnostic station. For the data, the length of the horizontal bar indicates the signal amplitude measured for the phase space coordinate at the right edge of each bar. For the simulation, the central group of contour lines (10% intervals) includes the distribution of two of the four merged beams in this projection of phase space.

Figure 6

Vertical phase space measurement (bottom panel) versus PIC simulation (top panel) at the $d3$ diagnostic station. For the data, the length of the horizontal bar indicates the signal amplitude measured for the phase space coordinate at the right edge of each bar. For the simulation (10% contour intervals), the higher density region near $y=0$, $y^{\prime }=0$ includes the distribution of two of the four merged beams in this projection of phase space.

Figure 7

Data (top panel) compared to PIC simulation (bottom panel) of the crossed-slit measurement at the $d3$ diagnostic station. The contour lines for the experimental data indicate 10% increments in relative intensity (20% contours for the PIC simulation) and the color code sequence from lowest to highest intensity is green, blue, yellow, pink,…, red.

Figure 8

Experimentally measured vertical phase space (top panel) versus PIC (bottom panel) at $d5$. The red box indicates for the simulation the region inside of which particles were included for the PIC (88%) emittance calculations of Table . The contour lines indicate 12.5% increments in relative intensity, and the color code sequence from lowest to highest intensity is yellow,…black. All of the PIC particles that lie outside of the lowest contour level are shown in order to illustrate the details of the calculated halo.

Figure 9

Horizontal phase space measurements (top panel) at $d5$ compared to the PIC simulation (bottom panel). The contour lines indicate 12.5% increments in relative intensity, and the color code sequence from lowest to highest intensity is yellow,…black. The red box indicates for the simulation the region inside of which particles were included for the PIC (88%) emittance calculations of Table , and the interior is approximately the same as the scanned boundary in the experiment. Approximately 7% of the PIC particles lie outside of this box. An additional 5% of the initial particles are lost in the simulation upstream when the particles strike a focusing electrode.

Figure 10

Data (top panel) compared to PIC simulation (bottom panel) of the crossed-slit measurement at the $d5$ diagnostic station. The contour lines indicate 12.5% increments in relative intensity, and the color code sequence from lowest to highest intensity is yellow,…black.

Figure 11

Evolution of emittance from the PIC simulation (dashed line for ${\epsilon }_{nx}$, solid line for ${\epsilon }_{ny}$). The emittance is calculated for all surviving particles in the simulation (95% at $d5$). Upstream of the merging element ($QD5$), the emittance of one of the four (2.6 mA) identical beams is shown. Downstream of the merging element, the emittance of the $\approx 10\mathrm{mA}$ merged beam is shown. The locations of the $d4$ and $d5$ diagnostic stations are indicated. The $d5$ station is at the end of the region of rapid emittance growth. The points below the curve are for the experimental data at $d4$ and $d5$ ($\mathrm{cross}={\epsilon }_{nx}$, $\mathrm{circle}={\epsilon }_{ny}$). The values $\epsilon (4i{)}_n$ and $\epsilon (4f{)}_n$ are from the analytical model described in the text.