NON-DESTRUCTIV SINGLE PASS MONITOR OF LONGITUDINALCHARGE DISTRIBUTION
P.V. Logatchov, P.A. Bak, A.A. Starostenko, N.S. Dikansky, E.A. Gousev, M.B. Korabelnikov,
A.R. Frolov, S.V. Shiyankov, BINP, Novosibirsk, Russia.

Abstract
This paper contains the present development ofa non-destructive method for intensive relativistic bunch
diagnostic. The method is based on the scanning of thethin electron beam within the energy range 20-100 kV inthe electromagnetic field of an intensive relativisticbunch. We used to inject the probe beam across the pathof relativistic bunch. This type of an electron beamprobe is suitable for both circular and linear accelerators.
The prototype results obtained on the VEPP-3 storage
ring and on the electron linac of VEPP-5 injector
complex at BINP have found out some new features ofthis non-destructive single bunch diagnostic tool. It isable to investigate not only the longitudinal charge
distribution in the bunch [1,2], but also the transverse
one. It is also sensitive to the transverse motion inside
the bunch [3] and, it can even feel wake-fields after thebunch.

1 THEORY
The thin probe beam moves along X-axis that isorthogonal to the direction of the relativistic bunch
motion (Z-axis), with the offset parameter ρ (see Fig.1).
ΑΒ

Xβ}

r−+∞

ρ 2 + ( x + βz ) 22 ρre n( z )[1 − e 2σ r ]dz
θ y ( x) =(1),βγ −∫∞ρ 2 + ( x + βz ) 2
where re is the classical electron radius, β = v / c and2γ = 1 / 1 − β 2 corresponds to the probe beam, c - thevelocity of light, x - the coordinate of testing beamparticle at t=0, n( z ) is the relativistic bunch linear
density along Z-axis in the lab. system. The expression
for the deflecting angle of the particle in Z direction due
to magnetic field can be written in a similar way:−+∞ρ 2 + ( x + βz ) 22r ( x + βz )n( z )[1 − e 2σ r
θ z ( x) = e ∫γ −∞ρ 2 + ( x + βz ) 22]dz(2)

2 RESULTS
As a result, thin probe beam traces the closed curve on
the screen. The dependence θ y (x ) can be measured inexperiment [3] and n(z ) can be found as a solution of
the integral equation (1).

Y2σcertain probe beam particle. Then the total deflecting
angle in Y direction for every particle under theinfluence of the electric field of the relativistic bunch
can be expressed as:40

ρ
Z

30

0Current, [A]20

100Fig. 1: Simple scheme of the experiment.
The results of scanning are monitored on thescreen parallel to the Y-Z plane and positioned at thedistance L from Z-axis. Let the center of the relativisticbunch be located at the origin at time t=0 whereas theprobe beam has the uniform density along X and thediameter d<< ρ . Here we assume that σ r is thetransverse sigma of the round Gaussian relativistic bunch.
At the time t=0 every x -coordinate is assigned to the-10
0

10

20

30

40

50

Time, [ps]Fig. 2: Probe beam image on the screen and result of its
processing. Solid curve represents the solution of linear
system with 7x7 matrix sizes (error is about 20%). Dots
are a result of Gaussian curve fitting by special
procedure.

where σ l - longitudinal size of the relativistic bunch.
This limitation comes from the mathematical properties
of integral equation (1) and corresponding system of
linear equations. Actually this integral equation is anapproximation, since it can not take the longitudinal
modulation of the probe beam velocity in the interaction
region into account.
Fig. 3 represents dependencies of the solutionn(z ) deviation upon the parameter α = σ l β / σ t fordifferent value of θ y (x ) deviation (A and B) andnumber of equations in corresponding linear system –the matrix size nxn. In order to improve resolution onecan reduce offset parameter ρ up to transverse
relativistic bunch size σ t . Since the useful value ofparameter αdepends

ontheerrorinθ y (x )measurement, and this error strongly connected to thequality of the probe beam, the temporal resolution in thisapproach is limited by the probe beam spot size on thescreen [4] and by the relativistic bunch shape. If
transverse relativistic bunch size is close to thelongitudinal one, the temporal resolution becomes verypoor.
BA

100

100

But there is another way to evaluate the longitudinalbunch size at low α values. It comes from the idea touse head on collision with zero offset parameter forprobe beam. Equations (1), (2) can be used forinvestigation of the image on the screen. Actually theimage is formed by three factors: the transverse
distribution in the probe beam at interaction point,
transverse and longitudinal distribution in relativistic
bunch, the probe beam offset parameter. If transverse
probe beam size at the interaction point grater, thantransverse relativistic bunch size, the image on thescreen will have a sharp border of elliptical shape forzero offset parameter. Thus it is possible to measure thevertical and horizontal size of the image. Both of thesesizes are proportional to the number of particles in thebunch. So the ratio of the vertical size to horizontal one
is independent upon the bunch intensity and sensitive tothe transverse and longitudinal bunch density
distribution (see Fig. 4).
A5
4.5
0.7
0.6
0.5
0.4
0.3

Accuracy

Accuracy

10.1

0.1

0.01

0.01
0 0.5 1 1.5 2 2.5 3

trace 1
trace 2trace 3trace 432.52
1.5
1
00.2

0 1 2 3 4 5 6 7 8 90.1

trace 1
trace 2trace 3trace 1
trace 2trace 3trace 4trace 5trace 610143.50.500 1 2 3 4 5 6 7 8 910B

0.8

Image aspect ratio

less than 10% deviation in n(z ) only if σ l β > 3 ρ ,A-0.05, B- 0.01. Different traces correspond to the different
matrix sizes: 1-5x5, 2-7x7, 3-9x9, 4-11x11.

Beam sizes

Fig.2 shows the result of longitudinal charge distribution
measurement in the bunch of VEPP-5 injector linac. Thismeasurement is done at 35 keV of the probe beamenergy, with 3 mm offset parameter and 1.5 mm ofrelativistic bunch transverse sigma. Unfortunately thisapproach has a natural limitation for accuracy of thesolution n(z ) . For 5% deviation in θ y (x ) one can findFig. 4: Horizontal and vertical image sizes and image
aspect ratio versus parameter α .

0 0.5 1 1.5 2 2.5 3

trace 1
trace 2trace 3trace 4

Fig. 3: Accuracy of the solution n(z ) versus theparameter α for different accuracy of θ y ( x ) measurement:

There are the dependencies (see Fig.4) ofvertical size (traces 1,4,6) and horizontal one (traces2,3,5) on parameter α for three cases: 1) Using equations(1),(2) – traces 1,2; 2) Simulation for round Gaussianbunch in transverse plane – traces 3,4; 3) Simulation
for the round uniformly charged bunch – traces 5,6. Part
B gives the dependencies of image aspect ratio upon theα value for three mentioned above cases: 1) trace 1; 2)
trace 2; 3) trace 3. Simulation (cases 2 and 3) gives theafter the bunch train up to the several tens ofnanoseconds after the train. Then the brightness
amplitude and its spectrum are presented. These wakefields come from the accelerating structure andcorrespond to the longitudinal mode at the frequency of8714 MHz.

3A rb itra ry u n its

result of 3d motion in relativistic bunch fields. A
significant difference in aspect ratio is obvious fordifferent transverse charge distributions. These
calculations were done for 50 keV probe beam energy,transverse relativistic bunch sigma or radius 0.5 mm and9
number of electrons in a bunch 1.2⋅10 .
The picture on the screen is very sensitive totransverse displacement of the transverse distribution
center along the bunch. If the transverse displacement ofbunch center and transverse bunch size are smaller thenprobe beam size in the interaction point, it is possible toevaluate the bunch shifting by comparing the brightnessbalance upper and bellow the probe beam axis (seeFig.5). Fig. 5 shows the result of the probe beaminteraction with the bunch train of VEPP-5 injector linac
atpracticallyzerooffset
parameter.

210-1-2

1 ,41 ,61 ,82 ,02 ,22 ,42 ,62 ,83 ,03 ,2T im e , [n s ]10A rb itr a ry u n its

864200123456789101112131415

16

1718

1920

F re qu en c y , [G H z ]Fig. 5: Probe beam interaction with the bunch train ofVEPP-5 injector linac for zero offset parameter.
A linear scanning was applied to separate images fromdifferent bunches. The time interval between bunches isequal to 350 ps. This picture demonstrates transverse
oscillations in the bunch train. It is also possible tomeasure the maximum electric field value in each bunch,
if longitudinal and transverse bunch sizes are known.
The maximum vertical size of the bunch image is
proportional to the maximum electric field inside thebunch. Together with other diagnostics this measurement
can be useful.
Another interesting application of the linear
scanning of the probe beam is the wake fields
observation in accelerator vacuum chamber. Wake fields
propagating through the vacuum chamber modulate themotion of probe beam in horizontal direction. It can beseen as the brightness modulation of beam image on thescreen (see Fig.6). Upper line demonstrates the picture
produced by bunch train, which excites several highorder modes of accelerating structure. This picture wasdone at big offset parameter (about 10 mm) in order toput the time scale on the scanning line (350 ps per bin).
Down picture shows the wake fields influence on theprobe beam scanning line. This picture can be seen justFig. 6: Observation of the wake fields.

3 CONCLUSION
The experiments on VEPP-5 injector linac
demonstrated at least two new applications for electron
beam probe with linear scanning:
1. Head on collision multi bunch tomography.
2. Wake fields observation.

4 REFERENCES
1.John A. Pasour and Mai T. Ngo “Nonperturbing
Electron Beam Probe To Diagnose Charged-Particle
Beams”, Rev. Sci. Instrum. 63 (5), May 1992.
2. P.V. Logatchov at al. “Nondestructiv Diagnostic Tool
For A Monitoring Of Longitudinal Charge
Distribution In A Single Ultrarelativistic ElectronBunch”, PAC-99, New York, 29 March -2 April
1999.
3. A.A. Starostenko, P.A. Bak, Ye.A. Gusev, N.S.
Dikansky, P.V. Logatchov, A.R. Frolov, “Nondestructive singlepass bunch length monitor:experiments at VEPP-5 preinjector electronlinac”,EPAC-2000, Viena, 30 June – 4 July 2000.
4. P. V. Logatchov, “The tutorial No 3”JAS 2000,
JOINT CERN-JAPAN-JINR-RUSSIA-USA
ACCELERATOR SCHOOL, July 1 - 14 2000.