Rotating system for four-dimensional transverse rms-emittance measurements

Knowledge of the transverse four-dimensional beam rms parameters is essential for applications that involve lattice elements that couple the two transverse degrees of freedom (planes). Of special interest is the elimination of interplane correlations to reduce the projected emittances. A dedicated rotating system for emittance measurements (ROSE) has been proposed, developed, and successfully commissioned to fully determine the four-dimensional beam matrix. This device has been used at the high charge injector (HLI) at GSI in a beam line which is composed of a skew quadrupole triplet, a normal quadrupole doublet, and ROSE. Mathematical algorithms, measurements, and the analysis of errors and the decoupling capability for ion beams of ${{}^{83}\mathrm{Kr}}^{13+}$ at $1.4\mathrm{MeV}/\mathrm{u}$ are reported in this paper.

Figure 1

Rotating system for emittance measurements: a single-plane slit and grid emittance measurement device housed in a chamber which can be rotated around the beam axis. The total length of ROSE is 833 mm.

Figure 2

Setup of the beam line with ROSE. The beam enters from the left.

Figure 3

Sketch of the ROSE beam line with a rotatable slit/grid emittance scanner. All beam second moments are measured at location $f$. Applying the inverted transfer matrix they are transported backwards to location $i$ of the initial and constant beam matrix $C_i$. Full beam transmission between location $i$ and location $f$ is required.

Figure 4

Safety islands (blue dots) and the selected doublet settings (red dots) applied during the measurements.

Figure 5

Projected rms ellipses from measurements applying four or six measurements with the skew triplet being switched off. Red and blue ellipses indicate the beam matrices $\widehat{C}(4)$ and $\widehat{C}(6)$. The projected rms emittances and the Twiss parameters are indicated. The two matrices produce almost identical rms ellipses and feature similar eigen emittances and coupling parameters.

Figure 6

Projected rms ellipses from measurements applying four or six measurements with the skew triplet being switched on. Red and blue ellipses indicate the beam matrices $\tilde{C}(4)$ and $\tilde{C}(6)$. The projected rms emittances and the Twiss parameters are indicated. According to the rms ellipses in the projections, the rms ellipses look very similar but feature different eigen emittances and coupling parameters.

Figure 7

Relative frequencies of the coupled second moments with skews off, the upper and lower pictures indicate the results with errors applying four and six measurements, respectively. Blue columns indicate the coupled second moments with errors and red solid lines indicate fits using Gaussian functions. The modified coupled second moments are evaluated as $⟨xy⟩=-0.14\pm 0.14/-0.10\pm 0.14{\mathrm{mm}}^2$, $⟨x{y}^{\prime }⟩=-0.17\pm 0.08/-0.44\pm 0.08\mathrm{mm}\mathrm{mrad}$, $⟨x^{\prime }y⟩=-0.29\pm 0.15/-0.25\pm 0.15\mathrm{mm}\mathrm{mrad}$, and $⟨x^{\prime }{y}^{\prime }⟩=-0.22\pm 0.06/-0.12\pm 0.06{\mathrm{mrad}}^2$.

Figure 8

Relative frequencies of the coupled second moments with skews on, the upper and lower pictures indicate the results with errors applying four and six measurements. Blue columns indicate the coupled second moments with errors and red solid lines indicate fits using Gaussian functions. The modified coupled second moments are evaluated as $⟨xy⟩=-3.28\pm 0.39/-3.83\pm 0.38{\mathrm{mm}}^2$, $⟨x{y}^{\prime }⟩=-1.10\pm 0.13/-1.15\pm 0.13\mathrm{mm}\mathrm{mrad}$, $⟨x^{\prime }y⟩=-0.74\pm 0.24/-0.54\pm 0.24\mathrm{mm}\mathrm{mrad}$, and $⟨x^{\prime }{y}^{\prime }⟩=-1.52\pm 0.07/-1.52\pm 0.07{\mathrm{mrad}}^2$.

Figure 9

Relative frequencies of the eigen emittances with skews off. The upper and lower pictures indicate the results applying four and six measurements, respectively. Red and blue columns indicate the eigen emittances and blue and red solid lines indicate fits using Gaussian functions. Black dashed lines indicate the measured eigen emittances without errors, and black solid lines indicate the rms error spans. Applying error analysis, the eigen emittances are ${ϵ}_1=2.64\pm 0.27/2.64\pm 0.27\mathrm{mm}\mathrm{mrad}$ and ${ϵ}_2=1.65\pm 0.14/1.61\pm 0.14\mathrm{mm}\mathrm{mrad}$.

Figure 10

Relative frequencies of the eigen emittances with skews on. The upper and lower pictures indicate the results applying four and six measurements, respectively. Red and blue columns indicate the eigen emittances and blue and red solid lines indicate fits using Gaussian functions. Black dashed lines indicate the measured eigen emittances without errors, and black solid lines indicate the rms error spans. Applying error analysis, the eigen-emittances are ${ϵ}_1=2.43\pm 0.19/2.53\pm 0.20\mathrm{mm}\mathrm{mrad}$ and ${ϵ}_2=2.04\pm 0.17/1.98\pm 0.22\mathrm{mm}\mathrm{mrad}$.

Figure 11

Relative frequencies of the coupling parameters. The upper and lower pictures indicate the results applying Eq. (41) and Eq. (42). Red and blue columns indicate the values before and after decoupling and blue and red solid lines indicate fits using Gaussian functions. Applying the identical transfer matrix $R(4)$, the coupling parameters are reduced from $t=0.94\pm 0.21/1.06\pm 0.26$ to $t=0.05\pm 0.06/0.05\pm 0.05$.