Content from this work may be used under the terms of the CC-BY-4.0 licence (© 2023). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI

12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3

IBIC2023, Saskatoon, Canada
JACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 3 6

STUDY OF NON-DESTRUCTIVE BPM-BASED ENERGYMEASUREMENT OF THE CANADIAN LIGHT SOURCE LINAC
H. Shaker∗ , D. Bertwistle, E.J. Ericson1 , Y. Sigari1 , E. Soltan2
Canadian Light Source, Saskatoon, Canada
1also at the University of Saskatchewan, Department of Physics and Engineering Physics
2
also at the University of Saskatchewan, Department of Computer Science
Abstract
There is a plan in the Canadian Light Source (CLS) toreplace the current Linac with a new one from ResearchInstruments GmbH in mid-2024. The first straight sectionof LTB (Linac-To-Booster) was upgraded to have two BPMs
(Beam Position Monitors) with a 4.75 m drift between themand two phosphor screens were replaced by YAG screens.
A new BPM and a YAG-based screen station upgraded thefollowing 90-degree achromat beamline. These upgrades
help us to measure the current and future Linac beam parameters, including the beam twiss parameters, energy, andenergy spread. In this paper, we discussed how we could use
these three BPMs for non-destructive energy measurement,
which will be a part of the active energy correction system.

INTRODUCTION
Canadian Light Source’s current electron linear accelerator will be replaced with a new one by Research Instruments
GmbH in mid-2024 [1, 2]. As part of the project, the beamdiagnostic systems in the LTB were upgraded. Figure 1
shows the layout of LTB and where the current diagnosticcomponents were upgraded or new components added. A
new BPM, BPM2, added by pairing with the BPM1, measures the transversal position and momentum of the electron
beam in the BPM2 location. There is a long drift between
these two BPMs and one Steerer (ST0003-05), just 26.22 cm
before that, and its effect is negligible compared to a puredrift as calculated. VSC0003-01 and VSC0003-03 phosphor screens were replaced by one inch round YAG screens,and the camera was upgraded to a digital one. This helps
us to measure twiss parameters. Also, they can be used tocalibrate BPMs. A new VSC0003-06 screen was installedin the achromat beamline to measure energy and energy
spread destructively and be used as a reference to calibrate
the BPM3. An online non-destructive method for the energy
measurement is required for the energy monitoring by operators and potentially to use in an active energy correction
system, which uses a script which implement a negative feedback system to change the phase of the Linac accelerating
section to keep the energy constant. For this purpose, a newBPM, SLM0003-03 (BPM3), was installed in the achromat
beamline just before the new screen station and after theslit. The slit will be upgraded, as part of the project, forthe beam profile scanning and energy filtering. When wecombine these three BPMs together, as we suggest, we can∗ hamed.shaker@lightsource.ca

measure the energy non-destructively. The first two are tomeasure the transverse position and momentum of the beamjust before entering the achromat beamline in the locationof the BPM2. Then, using the transfer matrix between theBPM2 and the BPM3 and the location of the beam read by
the BPM3, we can find the energy of the electron beam.

TRANSFER MATRIX & NORMALIZED X
The position of the beam at BPM3, SLM0003-03, is afunction of the beam energy and the beam position andmomentum at the BPM2 location. Here we defined a newparameter, normalized horizontal position, or normalized
x, which is just a function of energy. To calculate that, weshould know the transversal position and momentum of thebeam in the BPM2 location. We can measure 𝑥1 and 𝑥2 andEq. (1) shows how we can calculate 𝑥2′ by knowing the drift
length between them, which is 4.7518 m.
𝑥1{ 2′ } = {𝑥20𝐷 𝑥1} { } ⇒ 𝑥2′ = (𝑥2 − 𝑥1 )/𝐷1 𝑥1′(1)Equation (2) shows the position and momentum at theBPM3 location, knowing the transfer matrix and the position and momentum at the BPM2 location. We used a3x3 transfer matrix which included the horizontal information and dispersion. Because of using linear elements, thevertical components are decoupled.
⎧ 𝑥3 ⎫⎧ 𝑥2 ⎫{ ′ }{ ′ }𝑥=𝑀⎨ 3 ⎬⎨ 𝑥2 ⎬{Δ𝑝/𝑝}{Δ𝑝/𝑝}⎩⎭⎩⎭(2)

Now we can define the normalized x which is equal toΔ𝑝/𝑝 as you can see in Eq. (3) and it is a function of horizontal beam position in three BPMs, the drift length between
BPM1 and BPM2 and the first row of the transfer matrix
between the BPM2 and BPM3.
𝑥3 = 𝑀11 ∗ 𝑥2 + 𝑀12 ∗ 𝑥2′ + 𝑀13 ∗ Δ𝑝/𝑝 =𝑀11 ∗ 𝑥2 + 𝑀12 ∗ (𝑥2 − 𝑥1 )/𝐷 + 𝑀13 ∗ Δ𝑝/𝑝 ⇒𝑥𝑛 ≡ [𝑥3 − 𝑀11 ∗ 𝑥2 − 𝑀12 ∗ (𝑥2 − 𝑥1 )/𝐷] /𝑀13 = Δ𝑝/𝑝
(3)
The BPM2 to BPM3 transfer matrix can be calculated byknowing the elements between two BPMs.
𝑀 = 𝑀𝐷4 ∗ 𝑀𝑄𝐹2 ∗ 𝑀𝐷3 ∗ 𝑀𝐵 ∗ 𝑀𝐷2 ∗ 𝑀𝑄𝐹1 ∗ 𝑀𝐷1 (4)WEP036438

07 Machine Parameter Measurements

12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3Figure 1: The LTB layout with BPMs positions, BPM1 (SLM0003-02), BPM2(SLM0003-01), BPM3(SLM0003-03) andscreens (VSC0003-01, VSC0003-03, VSC0003-06).
𝑀𝐷1−4 is a drift transfer matrix and 𝐷1−4 = 0.6849,0.45775, 1.54695, 0.7328 m is the drift length. 𝑀𝐵 is a
sector dipole transfer matrix, 𝜙 is the dipole angle and R isits radius. 𝜙 = 45∘ and R = 850 mm in our case. 𝑀𝑄𝐹1,2 isa focusing quadrupole transfer matrix, 𝜇 = √𝑘 which k is thequadrupole focusing strength and L is the quadrupole length.
Both quadrupole length is 166.1 mm. 𝑘 = 0.2148𝐼 1/m2 [3]and the first and second quadrupole coil current is 9.14 A and
28.35 A, respectively. Equations (5)–(7) show the transfermatrix for a drift, sector dipole and a focusing quadrupole,
respectively [4].
⎧1{𝑀𝐷1−4 = ⎨0{0⎩𝐷1−4
100⎫}
0⎬1}
⎭(5)

⎧ −1.8485{
𝑀𝑂𝐹𝐹 = ⎨−0.9149 (1/m){0⎩0.1918 m 1.9784 m⎫}−0.4460
0.7071 ⎬ (9)}01⎭

Now we can rewrite Eq. (3) using the 𝑀𝑂𝑁 transfer matrix,
which shows how we can calculate the normalized x basedon the current parameters.
(𝑥 −𝑥 )

𝑥𝑛 ≡21𝑥3 + 0.9643 ∗ 𝑥2 + 0.2553 m ∗ 4.7518
m= Δ𝑝/𝑝0.8533 m(10)

BPM CALIBRATION

Now we can calculate the total transfer matrix, using thementioned current parameters. It is easy to recalculate it
or it is part of the script to calculate energy and to do theenergy correction using different currents for quadrupoles.
Equation (8) shows the BPM2-BPM3 transfer matrix when
the achromat beamline middle quadrupole, QF0003-04, isON and in its nominal value. It is also practical for offline
measurement to turn this quadrupole off for a better energy
and energy spread measurement resolution. Equation (9)shows the transfer matrix when this quadrupole is off.

We must calibrate BPMs and do alignment corrections
based on the mechanical LTB coordinates survey [5] before implementing them in Eq. (10). We will start with theBPM2. As shown in Fig. 1, there is the VSC0003-03 screen,
294.7 mm after the BPM2. We use it as a reference since
it was grided, and we can directly see the beam profile dimension and position. There is a positive axial offset of
1.62 mm for BPM2 compared to this screen, as measured
mechanically during the LTB survey. We should consider
the offset and the drift to add to the measured position withthe BPM to find equivalent positions. We will use the BPM1
measured position to correct this drift to calculate 𝑥2′ using
Eq. (1). Also, the small effect of the ST0003-05X steerer
that was 262.2 mm before the BPM2 was calculated to correct the 𝑥2′ at the BPM2 location. Figure 2 shows the result.
The scanning was done using the ST0003-02X steerer. We
should also consider the negative axial offset of 0.835 mm
for BPM2 compared to BPM1. Then, we can use the following equation for BPM1-3 to find the horizontal position
based on the BPM x measurement.

⎧ −0.9643−0.2553 m 0.8533 m⎫{}−0.9920−0.6720 ⎬𝑀𝑂𝑁 = ⎨0.1700 (1/m)
{}
001⎩⎭

⎧
𝑥 = 2.59𝑥𝐵𝑃𝑀1 + 4.46 mm{{ 1𝑥2 = 2.59𝑥𝐵𝑃𝑀2 + 3.62 mm⎨{{⎩ 𝑥3 = 2.53𝑥𝐵𝑃𝑀3 − 11.53 mm⎧ 𝑐𝑜𝑠(𝜙)𝑅𝑠𝑖𝑛(𝜙){𝑀𝐵 = ⎨−𝑠𝑖𝑛(𝜙)/𝑅 𝑐𝑜𝑠(𝜙){00⎩⎧ 𝑐𝑜𝑠(𝜇𝐿){𝑀𝑄𝐹 = ⎨−𝜇𝑠𝑖𝑛(𝜇𝐿){0⎩𝑅(1 − 𝑐𝑜𝑠(𝜙))⎫}𝑠𝑖𝑛(𝜙)⎬}1⎭𝑠𝑖𝑛(𝜇𝐿)/𝜇 0⎫}𝑐𝑜𝑠(𝜇𝐿)
0⎬
01}
⎭(6)

(7)

(8)

(11)
WEP03607 Machine Parameter Measurements

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ISSN: 2 6 7 3 - 5 3 5 0d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 3 6

Content from this work may be used under the terms of the CC-BY-4.0 licence (© 2023). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI

12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3

IBIC2023, Saskatoon, CanadaJACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0
d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 3 6

We assumed BPM1 following the same calibration slope.
Measurement of the VSC0003-01 screen behind the BPM1
confirms that roughly. Also, the beam goes through a verysmall horizontal spanning in the BPM1, and then a slightslope change is negligible. The result of the BPM3 calibration also confirms this assumption since all these three
BPMs are similar.
Now, we should go to calibrate BPM3. For the BPM3,
we used the data of the VSC0003-06 screen by scanning theST0003-02X steerer and considered the drift and alignment
between the screen and the BPM. The data was taken when
the achromat beamline quadrupole was off for a better resolution. To correct the drift effect, we need to know the 𝑥3′ .
For that, we are using Eq. (9). The negative axial offset of0.644 mm for BPM3 compared to VSC0003-06 was also
considered. Figure 3 shows the calibration result. It shows
almost the same calibration factor of BPM1 and BPM2 buta negative polarity compared to them, Eq. (11).

we see the result in Fig. 4. Energy variation is about 0.07 %,below 0.1 %, which is the pulse-to-pulse energy jittering of
the current and the new Linac. The non-zero average energy
is arbitrary and depends on how we select the nominal energy, which is about 250 MeV. It shows our model works
well. Now, we can measure the energy by scanning the lastaccelerating structure phase. The last accelerating section isoperating off-crest as a tool to correct the total beam energyof the Linac. Figure 5 shows the result. The energy changes
linearly around the nominal phase (∼ 110.3∘ ), but we sawsome non-linearity below ∼ 104∘ . Although the energy correction script operates in the linear part, further study for
non-linear behaviour could be helpful.

Figure 4: Energy measurement resolution, 0.07%.

Figure 2: BPM2 calibration result.

Figure 5: Energy measurement by scanning the last accelerating section phase.
Figure 3: BPM3 calibration result.

ENERGY MEASUREMENT RESULT
Now, we have the tool to start energy measurement. First,
we checked the model by scanning the ST0003-02X steerer
without changing the beam energy. The VSC0003-06 shows
horizontal displacement of the beam profile, which we know
comes from the beam’s horizontal position and momentum
on the BPM2 location, not from the energy variation. Measuring BPM1-3 horizontal data and using Eqs. (10) and (11),CONCLUSION
The proposed BPM-based non-destructive energy measurement method shows a good resolution which is below
the machine energy jittering. Based on this method, we prepared a script to measure and correct the Linac total energy.
This script will be used for the new Linac, and operators
can monitor the long-term operation of the Linac. Further
non-linear studies will be helpful for more accurate energy
measurements.

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IBIC2023, Saskatoon, Canada
JACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 3 6

REFERENCES[1] “CLS Linac Final Design Report”, CLS, Saskatoon, Canada,Internal CLS-RI document, Mar. 2023.
[2] M. Boland et al., “Design of a new S-band 250 MeV electron linac with RF SLED compression for the CLS”, in Proc.
IPAC’23, Venice, Italy, May 2023.
doi:1018429/JACoW-IPAC2023-TUPL108[3] C. Baribeau, “Magnetic Measurements of LTB Quadrupole”,
CLS, Saskatoon, Canada, CLS internal report, Mar. 2023.
[4] K. Wille, The Physics of Particle Accelerators, An Introduction,Oxford University Press Inc., 2000.
[5] A. Janis, “LTB Diagnostic Survey Coordinates”, CLS, Saskatoon, Canada, CLS internal report, Apr. 2023.

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12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3