Accelerated Ion Energy Measurement by Means ofCirculating Electron Flow
B. Bogdanovitch, A. Nesterovitch
Moscow state physics engineering institute.
115409, Kashirskoe shosse, 31, Moscow, Russia.
The object of the report is the statement of the ion beam
average energy measurement method in high energy
accelerators. Primary transducer design and operation aredescribed.
Trajectories of ion (i) and electron (e) beams in two
magnetic field regions and the drift space between them
are shown in Fig.1. In the proposed method the ion beam is
injected into a uniform stationary magnetic field region
with length d (dashed line in Fig.1), where ions move on
circle orbits with radius Ri. Passing the first magnetic fieldregion the ions are deflected by the angle 2α from theoriginal trajectory, then the ions pass the drift space oflength l. After the second magnetic field region the ions arealso deflected by the angle 2α. Electrons are injected along
the ion beam axis in the drift space. The electron injection
can be carried out by means of the small-sized heatedcathode, or by ionization of residual gas.

The accuracy of th method may be characterized bydispersion D [1]:De =d Xe

De =

ηe B,

(2)

where ηe - electron charge e to mass m ratio,
B - quantity of magnetic field induction, supposed
equal in both regions.
From Fig.1 we can define quantity Xi, which characterizes the displacement of the ion spectrum line:

Di =

Ri

id2l ⋅dRi,(3)

Then we can get the expression for the dispersion:

α αRe

(1)

where Xe - displacement of the electron spectrum line in thedetection plane,V - velocity of analysed ions ( electron velocity).
It can be shown that this dispersion value is:

Xi ≈i,dVααle
Xi/2
Xei

Xi/2eFig.1 The scheme of particle movement.
The electron beam is bent into opposite direction by themagnetic field and gets to the ion beam trajectory again,
making recirculation. After injection electrons may have as
well equal as different velocities. Due to coulomb interaction electron and ion velocities become close to each otherin a short time. This effect was tested experimentally. The
measurement of the electron and the ion velocities wasperformed by means of a magnetic spectrometer. Theelectron spectrometer had higher accuracy and essentiallysmaller magnetic field induction, than the spectrometer forthe energy measurement of the ion and the electronvelocity.

l ⋅ d ⋅ ηi ⋅ BV2,

(4)

where ηi - ion charge Zie to mass mi ratio.
Comparing expressions (2) and (4) we can get therelation:

ηe R e 2,= 2⋅⋅Di
ηi l ⋅ dDe(5)where Re - radius of the electron circle orbit.
From expression (5) we can see, if significances of d, Reand l are comparable, so in this method the device resolution is 103-104 times higher than in the prototype under
the same conditions.
If electron and ion velocities are equal to each other,equality is right:

Ri = R e ⋅ηe.
ηi(6)Taking into account expression (6) we can get that thedisplacement Xi has the value ~ R e ⋅ η e ηi , it can notexceed 10-1-10-2 mm. If the transverse sizes of the electronand ion beams are about some mm, we can neglect value
Xi . It simplifies the realization of this method.

3172ieie
465Fig.2 The scheme of facility.

Period T is the time of the equilibrium state determination when electron and ion velocities become equal to eachother. We can get T from the expression (in Gauss system)[2]:T=
where β i =β i2 ⋅ δβ8 ⋅ π ⋅ c 3 ⋅ r e2 ⋅ L ⋅ n i

Vic,

(7)

- the relative ion velocity; c - the lightvelocity; δβ - initial relative electron velocity deviationfrom the established significance β=βi , re - electron beam
radius (supposed that the transverse size of the electron
beam does not exceed the ion one), L - coulomb logarithm,
ni - ion density, defining as:

ni =Ii2π ⋅ r e ⋅ Vi ⋅ z i ⋅ e,(8)

where Ii - ion current in the electron beam aperture.
For example, for a proton beam with the parameters:
βp=0.1, Ii=10µA and for an electron beam with theparameters: re=1mm, δβ=0.01, time T=2sec, for Ii=10mA
T=2msec.
The version of the facility shown in Fig.2 consists ofvacuum chamber 1, electron injector 2, pulsed powersystem 3 of the electron injector, magnet 4, transparent 5

and nontransparent 6 monitors of the beam gravity centre
measuring system, source of adjustable direct voltage.
The described facility works as follows. The ion beam
passes inside the vacuum chamber between magnets 4 andthrough the hole in the cathode of the electron injector 2
without practically no deflection from the injection direction. The negative voltage pulse with an amplitudedecreasing in time is supplied from the power system 3 tothe electron emitter. The electron emission is carried out
during this pulse by means of cold emission, either by asmall-sized heated cathode, or due to ionisation in the caseof a plasma emitter. The limited electron current is definedby the injector perveance P and may be equal to 10-100
mA.
However, the choice of current intensity is defined, incase of technical realization, by the compromise between
sensitivity and device resolution.
The process of determining the electron beam gravity
centre position (when the electron velocity is equal to theion velocity) may be carried out by means of any known
method of transparent diagnostics, for example, by meansof electrostatic pickup-electrodes. In this case, themeasuring error does not exceed 10-1 mm. A higher
accuracy may be achieved if the transparent monitor isonly used for registration of the moment when the electron
velocity becomes equal to the ion one. Then for thedefinition of the beam position the nontransparent monitor
of the probe is used. Furthermore the velocity of electrons
may be defined by means of the known stopping potential
method. Such technical decision may be easier, since thenontransparent monitor is not used in this method [1].
References[1] Moskalev V.A. et al., Izmerenie parametrov puchkov
zarjazhennyh chastits. M.: Atomizdat, 1980.
[2] Budker G.I. et. al., Electronnoe ohlazhdenie i novye
vozmozhnosti v fizike elementarnyh chastits. Uspechi fizicheskih nauk, t. 124, v. 4, 1978, s. 561595.