Matching the laser generated $p$ bunch into a crossbar-$H$ drift tube linac

Proton bunches with energies up to 30 MeV have been measured at the PHELIX laser. Because of the laser-plasma interactions at a power density of about $4\times {10}^{19}\mathrm{W}/{\mathrm{cm}}^2$, a total yield of $1.5\times {10}^{13}\mathrm{protons}$ was produced. For the reference energy of 10 MeV, the yield within $\pm 0.5\mathrm{MeV}$ was exceeding ${10}^{10}\mathrm{protons}$. The important topic for a further acceleration of the laser generated bunch is the matching into the acceptance of an rf accelerator stage. With respect to the high space charge forces and the transit energy range, only drift tube linacs seem adequate for this purpose. A crossbar $H$-type (CH) cavity was chosen as the linac structure. Optimum emittance values for the linac injection are compared with the available laser generated beam parameters. Options for beam matching into a CH structure by a pulsed magnetic solenoid and by using the simulation codes LASIN and LORASR are presented.

Figure 1

Dependence of differential particle yield on energy for PHELIX experiment [16].

Figure 2

Schematic view of the laser target, the focusing solenoid, and the drift to the rf linac. The longitudinal axis is marked in mm and in ps time of flight for a 10 MeV on axis proton. Additionally, the range of LASIN and LORASR code based simulations are indicated.

Figure 3

Longitudinal (left) and transverse (right) components of the solenoidal field along the axis for different radii in cm; the geometric length of the solenoid (cyan lines) as well as the target position (brown line) are marked.

Figure 4

Output rms emittance in $x\mathrm{\text{−}}{x}^{\prime }$ versus $\Delta p/p$ (left); output to input rms-emittance ratio in $x\mathrm{\text{−}}{x}^{\prime }$ plane versus $\Delta p/p$ (right) at different opening angles, 210 mm behind of the target.

Figure 5

Input and output distributions in $x\mathrm{\text{−}}{x}^{\prime }$ for a monoenergetic beam with a divergence of $\pm 180\mathrm{mrad}$ (left), and for a beam with $\Delta p/p=\pm 10\%$ at $\pm 90\mathrm{mrad}$ (right).

Figure 6

The $xy$ (left) and $x{x}^{\prime }$ (right) projections of the $10\pm 0.5\mathrm{MeV}$ fraction of a simulated proton pulse after 10 ps; ${\epsilon }_{rms}=6.56\mathrm{mm}\mathrm{mrad}$.

Figure 7

Transversal density profile of the particle pulse.

Figure 8

$z\mathrm{\text{−}}x$ projection of the particle distributions after 25 ps. The action of the magnetic solenoid fringing field is seen already. Particle energies of interest for acceleration are marked in green.

Figure 9

Potential curves in longitudinal (left) and transversal (right) directions at three different positions along $z$. At $t=40\mathrm{ps}$, the space charge potential is reaching a maximum.

Figure 10

Detail of the potential curve (from Fig. 9) after 17.5 ps in the longitudinal direction. The plasma oscillation has a higher potential fluctuation at lower $z$ positions, where the simulated particle density is higher.

Figure 11

Time evolution of the electron energy distribution. The right picture for $t\ge 17.5\mathrm{ps}$ has different scales.

Figure 12

Proton (red) and electron (blue) distribution in the $z\mathrm{\text{−}}x$ plane after 460 ps. Electrons are accelerated axially by their own potential. The detail AB containing the whole proton distribution is shown on the right. The green marked area corresponds to the protons with $10\mathrm{MeV}\pm 0.5\mathrm{MeV}$.

Figure 13

The $x\mathrm{\text{−}}{x}^{\prime }$ phase space projection of the whole transported proton spectrum with $10\mathrm{MeV}\pm 5\mathrm{MeV}$ at 460 ps. The pronounced core structure is dominated by the lower energy protons (compare with Figs. 12, 15).

Figure 14

Transversal proton distribution for the energy band $10\mathrm{MeV}\pm 0.5\mathrm{MeV}$ after 460 ps.

Figure 15

Proton distribution $x\mathrm{\text{−}}{x}^{\prime }$ for the energy band $10\mathrm{MeV}\pm 0.5\mathrm{MeV}$ after 460 ps. The local influence of electrons comoving on the axis is seen at $|x|<0.5\mathrm{mm}$.

Figure 16

Proton spectral distribution development within the first 460 ps. The shape is changing mainly at the low energy end.

Figure 17

(Left) $z\mathrm{\text{−}}x$ proton distribution after the solenoid. The longitudinal position is correlated to the individual proton energies. (Right) $x\mathrm{\text{−}}{x}^{\prime }$ distribution for the same propagation time $t=3.4\mathrm{ns}$. The green marked area corresponds to the energy of interest (see also Fig. 25 for a more detailed view).

Figure 18

A copper plated CH-DTL structure.

Figure 19

A schematic view of the CH-DTL, showing the separated function concept of the KONUS-beam dynamics.

Figure 20

Effective shunt impedance for different rf structures including the transit time factor $T$ and the synchronous phase ${\phi }_s$ as a function of the particle velocity $\beta =v/c$. The black horizontal bars represent some realized interdigital $H$-mode (IH)-DTL’s while the blue line represents the expected shunt impedance from IH cavities. The red line represents the expected shunt impedance of the room temperature CH cavities for the GSI-FAIR 70 MeV, 70 mA proton linac [26].

Figure 21

Schematic diagram of a crossbar $H$-mode structure (CH) showing the electric fields in red and the magnetic fields in blue (courtesy of Rudolf Tiede).

Figure 22

3D view on the proposed CH-DTL consisting of four rf cavities separated by triplet quadrupoles. In front of the first cavity, the pulsed solenoid is located and the distance between the end edge of the solenoid and the center of the first gap is 103 mm.

Figure 23

Transverse 90%, 99%, and 100% envelopes at 500 mA beam current. Black lines indicate the aperture.

Figure 24

Transverse (left) and longitudinal (right) particle distribution at entrance and exit of the CH-DTL section at 500 mA equivalent beam current. The input and output energies of the CH-DTL were 10 and 40 MeV, respectively. Normalized emittance values are relevant for the plotted 95% ellipses.

Figure 25

Laser generated particle distribution in transversal (left) and longitudinal (right) planes at the DTL entrance within an energy range $10\mathrm{MeV}\pm 0.5\mathrm{MeV}$ in green (identical with the green distribution of Fig. 17, right). The red 72% subset falls within the transverse CH-DTL acceptance area and is used for DTL beam dynamics simulations.

Figure 26

Transverse 90%, 95%, and 100% beam envelopes starting 60 mm behind the solenoid. Black lines indicate the aperture.

Figure 27

Output transversal (left and middle) and longitudinal (right) particle distribution at the CH-DTL structure exit where the output energy is 40 MeV. The input particle distributions are shown in Fig. 25 (the red subset).