Parameters Values
Bore radius 25.654 mm
Length 0.1 m
Yoke inner radius 145 mm
Yoke thickness 25.4 mm
Yoke material Zinc plating 1018 steel Pole thickness 17.99 mm
Pole material Zinc plating 1008 steel
AWG 12
Wire turn per pole 150
Table 2: Specification of the homemade octupole magnet.
Based on the physics design, Scott finished the engineering design and ordered the yoke and poles fabrication [see Fig. 18(a)]. Using a wire winding machine, we winded the eight poles with AWG 12 wire. Assembled homemade octupole magnet is shown in Fig. 18(c) and detailed specifications are presented in Table 2. Before the homemade octupole installation in the beamline, we measured saturation current [Fig. 18(d)] and the magnetic field on the horizontal axis [Fig. 18(e)]. The octupole seems to have saturation current at 2 A, but it is close to linear line until the current of 3 A. When applied current is 3 A, the field has nice third-order trend compared to the simulation and its third-order coefficient from the cubic fitting is 5566 T/m3. Note, we had a mistake on maximum octupole field strength. The required strength was only∼2000 T/m3while our homemade octupole has the 3 times stronger field strength.
The stronger field strength is no problem in our experiment.
beam properties. As referred previously, the LPS diagnostic section are following after the DEEX beam- line. It projects LPS to transverse plane so that we can see LPS through the camera. Here, we present details of these diagnostic methods for our experiment.
4.2.1 YAG screen
Cerium-doped Yttrium aluminum garnet (YAG:Ce) and optical transmission radiation (OTR) are general methods to measure the transverse beam image. Both methods emit lights which can be transported to the CCD camera using optical components. However, the YAG:Ce uses scintillation while OTR emits the light via transition. AWA adopts YAG:Ce as the screen (see Fig. 19). One drawback of the YAG screen is saturation at high charge beam. In this situation, OTR may be useful because it has low photon flux production than the YAG.
Figure 19: YAG screen used in the AWA beamlines. Yellow circle is YAG:Ce. Beyond the YAG, 45◦ mirror is installed to reflect the emitted light to out of the beamlines.
4.2.2 Quadrupole scan
The experiment requires specific horizontal phase space conditions to the first EEX beamline entrance and the second EEX beamline entrance. This condition will be matched using quadrupoles in the beam- line. Although the beam behavior after the quadrupole is well matched with the transfer matrix, we have to know initial condition to the quadrupole entrance. The general method to measure the transverse beam properties is quadrupole scan that obtains Twiss parameters. The method scans the quadrupole gradient and measures the changes of beam size on a downstream screen. Because transfer matrix for the quadrupole scan is already known, we could achieve Twiss parameters based on the transfer matrix.
Below is transfer matrix of the quadrupole scan.
R=Rdrift·Rquad
=
1 d 0 0
0 1 0 0
0 0 1 d
0 0 0 1
·
cos lq g
Bρ
q
Bρ g sin
lq g
Bρ
0 0
−q g
Bρsin
lq g
Bρ
cos
lq g
Bρ
0 0
0 0 cosh
lq g
Bρ
q
Bρ g sinh
lq g
Bρ
0 0 q g
Bρsinh
lq g
Bρ
cosh
lq g
Bρ
(4.3)
=
R11 R12 0 0 R21 R22 0 0 0 0 R33 R34 0 0 R43 R44
, (4.4)
where
R11=cos
l r g
Bρ
−d r g
Bρsin
l r g
Bρ
, (4.5)
R12= s
Bρ g sin
l
r g Bρ
+dcos
l
r g Bρ
, (4.6)
R21=− r g
Bρsin
l r g
Bρ
, (4.7)
R22= s
Bρ g sinh
l
r g Bρ
+dcosh
l r g
Bρ
, (4.8)
R33=cosh
l r g
Bρ
+d r g
Bρsinh
l r g
Bρ
, (4.9)
R34= s
Bρ g sinh
l
r g Bρ
+dcosh
l r g
Bρ
, (4.10)
R43= r g
Bρsinh
l r g
Bρ
, (4.11)
R44=cosh
l r g
Bρ
. (4.12)
Here,d is the length between the quadrupole and the screen,lis the effective length of the quadrupole, Bρis the magnetic rigidity of the beam, andgis the gradient of the quadrupole.
The screen only can provide horizontal and vertical rms beam sizes. Hence, we need to consider the analytical beam sizes at the screen based on the transport equation.
σx,2f =σx,i2(R11+sxR12)2+R212εx,i2
σx,i2 , (4.13)
σy,2f =σy,i2(R33+syR34)2+R234εy,i2
σy,i2 , (4.14)
where indicesiand f indicate the quadrupole entrance and the screen, respectively. These equations are applied to the experimental measurements. For instance, if we scanned the quadrupole gradient froma T/m tobT/m withnpoints and measured both horizontal and vertical beam sizes at each point, initial beam sizes, slopes and emittances are unknown factors in the equations. To find these unknown factors, we apply parametric fitting on the measurement data based on these equations. Fitting coefficients of the parametric fitting should be these unknown factors. The fitting returns the coefficients so that we can calculate the initial Twiss parameters as,
αx,i=−sx,iσx,i2
εx,i , (4.15)
βx,i=σx,i2
εx,i, (4.16)
γx,i=1+αx,i2 βx,i
. (4.17)
Vertical Twiss parameters hold same arguments. Note that the quadrupole scan is better to contain focal point to increase of the fitting accuracy.
4.2.3 LPS diagnostic section
An LPS measurement was performed by projecting the longitudinal beam distribution onto a transverse plane using a TDC and spectrometer. The TDC applies a time-varying vertical kick to the beam accord- ing to the longitudinal position of the beam, and the spectrometer bends the beam horizontally according to its energy. This projection-based measurement requires a multiplication factor to convert measured data to actual time and energy data. The measured multiplication factors for the temporal and spectral measurement were 2.872 and 0.365, respectively. The aim is to have only longitudinal properties appear on the transverse screen. Therefore, it is important to minimize the contribution of the beam’s transverse phase space to improve the measurement resolution. This was achieved in two ways. First, quadrupole magnets in front of the TDC focused the beam in both the horizontal and vertical directions. Second, the horizontal slit was applied to the beam to minimize the inevitable correlation error that the measurement system introduces. Further details are provided in Ref. [53]. Although the transverse phase spaces were minimized, the beam still has some transverse contributions which determine the resolutions of system.