Longitudinal charge distribution measurement of nonrelativistic ion beams using coherent transition radiation

Longitudinal charge profile measurements or bunch shape measurements are a challenge for temporally short nonrelativistic bunches. The field profile has a larger longitudinal extent compared to the charge profile for such beams. This affects the ability of field sensing devices such as phase pickups or wall current monitors to measure charge distribution. Here we evaluate the feasibility for usage of coherent transition [V. L. Ginzburg and V. N. Tsytovich, Transition Radiation and Transition Scattering (Adam Hilger, New York, 1990)] and diffraction radiation from nonrelativistic beams for single shot bunch shape measurements in the time domain.

Figure 1

Coordinate system and the target plane.

Figure 2

(a) Comparison of normal incident radiation (NIR), quasispherical approximation (QSA) and far field approximation (FFA) for $\beta =0.3$ for target radius $b=0.4\mathrm{m}$, monitor distance $R=0.4\mathrm{m}$ and $\mathrm{frequency}=0.7\mathrm{GHz}$. (b) Comparison of NIR, QSA and FFA for target radius $b=1.2\mathrm{m}$, monitor distance $R=1.2\mathrm{m}$ at $\beta =0.99$.

Figure 3

(a) Frequency response as a function of target size for $\beta =0.05$ at monitor distance $R=2.0\mathrm{m}$. (b) Frequency response as a function of target size for $\beta =0.9$ at monitor distance $R=2.0\mathrm{m}$.

Figure 4

Electric field spectral amplitude dependence on target size.

Figure 5

The angular distributions 0.3 and 5.7 GHz for $\beta =0.99$ as a function of monitor distance from the target. The target size is set to $1.4\beta \gamma \lambda$ for the reference wavelength of ${\lambda }_{\mathrm{ref}}=1\mathrm{m}$. Equation (13) scaled with $2\pi$ is shown as dotted lines which separate wave and prewave zone.

Figure 6

Percentage error between 0.3 and 5.7 GHz for $\beta =0.99$ as a function of monitor angle and distance from the target. The target size is set to $1.4\beta \gamma \lambda$ for the reference wavelength of ${\lambda }_{\mathrm{ref}}=1\mathrm{m}$. Above 2 m radial distance, the radiation has a far field like distribution for the relevant frequency range for angles larger than 60°.

Figure 7

(a) Frequency response as a function of hole size for $\beta =0.15$ at monitor distance $R=1.0\mathrm{m}$. Frequency spectrum of a 100 ps bunch is marked with dashed lines. (b) Calculated electric field for a broadband detector at 85° for an input of 100 ps bunch for different hole sizes in the target.

Figure 8

The simulation model.

Figure 9

(a) Time domain snapshot of all three components of the transition radiation electric field for beam velocity $v=\beta ·c$ where $\beta =0.15$. (b) Field amplitudes as a function of monitor angle obtained from cst in comparison with NIR.

Figure 10

Absolute TR electric fields at four monitors placed at incremental distances from the target at (a) 45° and (b) 80° angles for $\beta =0.6$. The dashed line represents $1/r$ dependence.

Figure 11

Comparison of analytical and simulation angular field distribution at the peak field obtained for different velocities at $R=1.0\mathrm{m}$ distance for a 100 ps bunch.

Figure 12

The angular distribution for the peak field obtained for a 100 ps bunch at $\beta =0.9$ and $\beta =0.99$ as a function of monitor distance from the target. The target size is set to $1.4\beta \gamma \lambda$ for the reference wavelength of $\lambda =1\mathrm{m}$.

Figure 13

(a) Obtained radiation (absolute values of E field) as a function of target size for $\beta =0.6$ at monitor distance $R=0.4\mathrm{m}$ at 45 degrees. (b) Selected region to highlight the differences.

Figure 14

(a) Obtained radiation (z component of E field) as a function of hole size for $\beta =0.15$ at monitor distance $R=1.0\mathrm{m}$ at 85 degrees for an input of $100\mathrm{ps}$ $\sigma$ bunch for different hole sizes. (b) Zoomed out view of the plot on the left.

Figure 15

(a) Photo of the first prototype setup. (b) The simulation model of the setup (cross section).

Figure 16

(a) cst simulation output showing the $\overrightarrow{E_z}$ component at the broadband monitor of the model shown in Fig. 15 for 100 ps Gaussian charge distribution traversing with velocity $\beta =0.15$. (b) Enlarged section around the bunch signal.

Figure 17

(a) Two consecutive bunches measured by a pickup and GHz transition radiation monitor spaced apart by 2 m. (b) Enlarged view focusing on the second bunch.

Figure 18

Bunch length measurement for three consecutive macropulses by GTR (top row) and pickup (bottom row).

Figure 19

Schematic of a charge passing by a monitor towards a target where it is normally incident.

Figure 20

Ratio of direct field against transition radiation field as a function of monitor distance from target for two monitor angles.

Figure 21

(a) Magnitude response and (b) Phase response calculated from S11 measurement.