Helical coil design with controlled dispersion for bunching enhancement of protons generated by the target normal sheath acceleration

The quality of the proton beam produced by target normal sheath acceleration (TNSA) with high-power lasers can be significantly improved with the use of helical coils. While they showed promising results in terms of focusing, their performances in terms of the of cut-off energy and bunching stay limited due to the dispersive nature of helical coils. A new scheme of helical coil with a tube surrounding the helix is introduced, and the first numerical simulations and an analytical model show a possibility of a drastic reduction of the current pulse dispersion for the parameters of high-power-laser facilities. The helical coils with tube strongly increase bunching, creating two collimated narrow-band proton beams from a broad and divergent TNSA distribution. The analytical model provides scaling of proton parameters as a function of laser facility features.

Figure 1

Scheme of (a) helical coil with tube and (b) broadband high-power pulsed helix TWT [40].

Figure 2

Dependence of the current frequency (a) and phase velocity (b) on the wave number for a HC of radius $a=0.5$ mm, pitch $h=0.35$ mm, with tubes of different radii and without tube.

Figure 3

Mesh of a HC with tube in SOPHIE. The target is in cyan, the helical coil in red, and the target holder and tube in purple.

Figure 4

PIC simulation of the current pulse intensity in kA for a helical coil (a) without tube and (b) with tube as a function of time and along the HC axis. The particles features are defined in Table 1 for ALLS. The HC parameters are length $L=40$ mm, radius $a=0.5$ mm, wire thickness of 0.02 mm, and pitch $h=0.35$ mm with a tube of radius $b=0.9$ mm. The dashed line corresponds to $V_{\mathrm{HC}}$, the geometrical speed of the HC, the dash-dotted line corresponds to $V=1.2V_{\mathrm{HC}}$.

Figure 5

Phase velocity normalized by the geometrical speed of the helix as a function of the wave number for a HC of radius $a=0.5$ mm, pitch $h=0.35$ mm, with tubes of different radii.

Figure 6

PIC simulation of the current pulse intensity in kA for a helical coil (a) without tube and (b) with tube as a function of time and along the HC axis. The particles features are defined in Table 1 for LULI2000. The HC parameters are length $L=40$ mm, radius $a=0.5$ mm, wire thickness of 0.02 mm, and pitch $h=0.35$ mm with a tube of radius $b=0.9$ mm. The dashed line corresponds to $V_{\mathrm{HC}}$, the geometrical speed of the HC, and the dash-dotted line corresponds to $V=1.2V_{\mathrm{HC}}$.

Figure 7

(a) Schematics of the model DoPPLIGHT. (b) Schematics of the helix fields calculation module in DoPPLIGHT.

Figure 8

DoPPLIGHT calculation of the current pulse intensity in kA for a helical coil (a) without tube and (b) with tube as a function of time and along the HC axis. The particles features are defined in Table 1 for ALLS. The current is defined analytically by a Gaussian function with FWHM ${\tau }_{\mathrm{FWHM}}=3$ ps and amplitude at $z=0$ mm $I_0=7$ kA, delayed with respect to the particule emission by 6 ps. The HC parameters are length $L=40$ mm, radius of the thin cylinder $a=0.5$ mm, and pitch $h=0.35$ mm with a tube of radius $b=0.8$ mm. The dashed line corresponds to $V_{\mathrm{HC}}$, and the dash-dotted line corresponds to $V=1.2V_{\mathrm{HC}}$.

Figure 9

DoPPLIGHT calculation of the current pulse intensity in kA for a helical coil (a) without tube and (b) with tube as a function of time and along the HC axis. The particles features are defined in Table 1 for LULI2000. The current is defined analytically by a Gaussian function with FWHM ${\tau }_{\mathrm{FWHM}}=8.5$ ps and amplitude at $z=0$ mm $I_0=30$ kA, delayed with respect to the particule emission by 6 ps. The HC parameters are length $L=40$ mm, radius of the thin cylinder $a=0.5$ mm, and pitch $h=0.35$ mm with a tube of radius $b=0.8$ mm. The dashed line corresponds to $V_{\mathrm{HC}}$, and the dash-dotted line corresponds to $V=1.2V_{\mathrm{HC}}$.

Figure 10

Longitudinal field on the HC axis at different times, dashed lines correspond to an HC without tube, full lines to an HC with tube. The particles features set are defined in Table 1 for ALLS. The HC parameters are length $L=40$ mm, radius $a=0.6$ mm, wire thickness of 0.02 mm, and pitch $h=0.35$ mm with a tube of radius $b=1$ mm.

Figure 11

Spectra of accelerated protons: (a) TNSA spectrum (green line), spectrum at the exit of an HC without tube (blue line) and spectrum at the exit of an HC with tube (orange line) in PIC simulations, (b) spectrum at the exit of an HC with tube in PIC simulations (orange line) and in the numerical model DoPPLIGHT (red line). The particles features are in Table 1 for ALLS. The HC parameters are length $L=40$ mm, radius $a=0.5$ mm, wire thickness of 0.02 mm, and pitch $h=0.35$ mm with a tube of radius $b=0.9$ mm, and the HC characteristic energy is 2.9 MeV.

Figure 12

Scaling of the energy of the bunch with respect to the HC characteristic energy normalized by the input cut-off energy: (a) normalized energy of the most energetic bunch, (b) normalized energy of the least energetic bunch, (c) normalized energy of the depletion zone. Colored dots correspond to DoPPLIGHT calculations, black squares to PIC simulations. Color code shows dependence on the coil radius. All HC are with tube.

Figure 13

Yield of protons at the exit of HC with tube as a function of the HC characteristic energy divided by the input cut-off energy; color code shows dependence on the coil radius.

Figure 14

Proton energy spectrum at the exit of a cone of radius $a=0.5$ mm and length $L=40$ mm calculated with DoPPLIGHT with only space charge fields for an ALLS-based input spectrum, as defined in Table 1.

Figure 15

PIC simulation of the current pulse intensity in kA for a helical coil (a) without tube and (b) with tube as a function of time and along the HC axis. The particles features are defined in Table 1 for ALLS. The HC parameters are length $L=40$ mm, radius in the heart of the coil $a=0.6$ mm, external $\mathrm{radius}=0.7$ mm, and step $h=0.3$ mm with a tube of radius $b=1$ mm. The dashed line corresponds to $V_{\mathrm{HC}}$, the geometrical speed of the HC, and the dash-dotted line corresponds to $V=1.2V_{\mathrm{HC}}$.

Figure 16

DoPPLIGHT calculation of the current pulse intensity in kA for a helical coil (a) without tube and (b) with tube as a function of time and along the HC axis. The particles features are defined in Table 1 for ALLS. The current is defined analytically by a Gaussian with FWHM ${\tau }_{\mathrm{FWHM}}=3$ ps and amplitude at $z=0$ mm $I_0=7$ kA, delayed with respect to the particule emission by 6 ps. The HC parameters are length $L=40$ mm, radius of the thin cylinder $a=0.6$ mm and step $h=0.3$ mm with a tube of radius $b=0.9$ mm. The dashed line corresponds to $V_{\mathrm{HC}}$, and the dash-dotted line corresponds to $V=1.2V_{\mathrm{HC}}$.

Figure 17

PIC simulation of the current pulse intensity in kA for a helical coil (a) without tube and (b) with tube as a function of time and along the HC axis. The particles features are defined in Table 1 for LULI. The HC parameters are length $L=40$ mm, radius in the heart of the coil $a=0.6$ mm, external radius=0.7 mm, and step $h=0.3$ mm with a tube of radius $b=1$ mm. The dashed line corresponds to $V_{\mathrm{HC}}$, the geometrical speed of the HC, and the dash-dotted line corresponds to $V=1.2V_{\mathrm{HC}}$.

Figure 18

DoPPLIGHT calculation of the current pulse intensity in kA for a helical coil (a) without tube and (b) with tube as a function of time and along the HC axis. The particles features are defined in Table 1 for LULI. The current is defined analytically by a Gaussian with FWHM ${\tau }_{\mathrm{FWHM}}=8.5$ ps and amplitude at $z=0$ mm $I_0=30$ kA, delayed with respect to the particule emission by 6 ps. The HC parameters are length $L=40$ mm, radius of the thin cylinder $a=0.6$ mm, and step $h=0.3$ mm with a tube of radius $b=0.9$ mm. The dashed line corresponds to $V_{\mathrm{HC}}$, and the dash-dotted line corresponds to $V=1.2V_{\mathrm{HC}}$.

Figure 19

PIC simulation of the current pulse intensity in kA for a helical coil (a) without tube and (b) with tube as a function of time and along the HC axis. The particles features are defined in Table 1 for LULI. The HC parameters are length $L=40$ mm, radius in the heart of the coil $a=0.5$ mm, external $\mathrm{radius}=0.6$ mm, and step $h=0.5$ mm with a tube of radius $b=0.9$ mm. The dashed line corresponds to $V_{\mathrm{HC}}$, the geometrical speed of the HC, and the dash-dotted line corresponds to $V=1.2V_{\mathrm{HC}}$.

Figure 20

DoPPLIGHT calculation of the current pulse intensity in kA for a helical coil (a) without tube and (b) with tube as a function of time and along the HC axis. The particles features are defined in Table 1 for LULI. The current is defined analytically by a Gaussian with FWHM ${\tau }_{\mathrm{FWHM}}=8.5$ ps and amplitude at $z=0$ mm $I_0=30$ kA, delayed with respect to the particule emission by 6 ps. The HC parameters are length $L=40$ mm, radius of the thin cylinder $a=0.5$ mm and step $h=0.5$ mm with a tube of radius $b=0.8$ mm. The dashed line corresponds to $V_{\mathrm{HC}}$, and the dash-dotted line corresponds to $V=1.2V_{\mathrm{HC}}$.