Thermal effects and beam parameter variations in electron guns
The paper describes results of research on influence of electrode temperatures and manufacturing tolerance of an electron gun on parameters of an output beam. The Pierce's gun that provides an electron beam with a current of 1.2 A and energy of 25 keV for the S-band technological linac is consi...
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| Veröffentlicht in: | Вопросы атомной науки и техники |
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| Datum: | 2001 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Zitieren: | Thermal effects and beam parameter variations in electron guns / I.V. Khodak, V.A. Kushnir, V.V. Mitrochenko, D.L. Stepin, V.F. Zhiglo // Вопросы атомной науки и техники. — 2001. — № 5. — С. 134-136. — Бібліогр.: 5 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859772324097556480 |
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| author | Khodak, I.V. Kushnir, V.A. Mitrochenko, V.V. Stepin, D.L. Zhiglo, V.F. |
| author_facet | Khodak, I.V. Kushnir, V.A. Mitrochenko, V.V. Stepin, D.L. Zhiglo, V.F. |
| citation_txt | Thermal effects and beam parameter variations in electron guns / I.V. Khodak, V.A. Kushnir, V.V. Mitrochenko, D.L. Stepin, V.F. Zhiglo // Вопросы атомной науки и техники. — 2001. — № 5. — С. 134-136. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The paper describes results of research on influence of electrode temperatures and manufacturing tolerance of an electron gun on parameters of an output beam. The Pierce's gun that provides an electron beam with a current of 1.2 A and energy of 25 keV for the S-band technological linac is considered as an example. Numerically calculated parameters of the beam and the temperature distribution in electrodes are presented. It is shown that the acceptable error in a position of electrodes is ±0.1 mm. This value does not fall outside the limit of thermal deformations and technical abilities for manufacturing guns in a laboratory. The scaling to the area of injectors for compact X-band linacs leads to the tolerance of ±0.01 mm that requires introducing fixing and adjustment elements reducing a thermal insulation of the cathode. However, the calculation and experiment showed that such reducing is negligible even for the modern low temperature thermionic cathodes due to a dominant role of the radiation in the heat transfer. This circumstance permits to create the precision intensive compact thermionic electron sources with replacing cathode for the compact linacs.
|
| first_indexed | 2025-12-02T06:36:51Z |
| format | Article |
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THERMAL EFFECTS AND BEAM PARAMETER VARIATIONS
IN ELECTRON GUNS
I.V. Khodak, V.A. Kushnir, V.V. Mitrochenko, D.L. Stepin, V.F. Zhiglo
National Science Center “Kharkov Institute of Physics & Technology”
1, Akademicheskaya St., NSC KIPT, 61108 Kharkov, Ukraine
e-mail: kushnir@kipt.kharkov.ua
The paper describes results of research on influence of electrode temperatures and manufacturing tolerance of an
electron gun on parameters of an output beam. The Pierce's gun that provides an electron beam with a current of
1.2 A and energy of 25 keV for the S-band technological linac is considered as an example. Numerically calculated
parameters of the beam and the temperature distribution in electrodes are presented. It is shown that the acceptable
error in a position of electrodes is ±0.1 mm. This value does not fall outside the limit of thermal deformations and
technical abilities for manufacturing guns in a laboratory. The scaling to the area of injectors for compact X-band
linacs leads to the tolerance of ±0.01 mm that requires introducing fixing and adjustment elements reducing a
thermal insulation of the cathode. However, the calculation and experiment showed that such reducing is negligible
even for the modern low temperature thermionic cathodes due to a dominant role of the radiation in the heat trans-
fer. This circumstance permits to create the precision intensive compact thermionic electron sources with replacing
cathode for the compact linacs.
PACS numbers: 29.25.Bx, 41.85.Ar
1 INTRODUCTION
Vacuum failures during operation of power electron
linacs reduce the lifetime of dispenser cathodes of the
electron guns. Obviously, the design of the gun with an
easy replaced cathode is rational in this case. The sim-
plification of a replacement operation requires a re-
search on the problem of a cathode installation toleran-
ce. This problem has significance under development of
a X-band linacs for radiation applications. It is possible
to show by simple scaling [1] that a transition to the
compact X-band linac will require the reducing of geo-
metric deviations proportionally to a frequency. There-
fore, an investigation of influence of gun geometry er-
rors on deviations of output beam parameters is impor-
tant.
Deviations from optimal geometry can arise at cath-
ode replacement as well as during heating of electrodes.
It may be a reason of known dependence [2] of a per-
veance and geometric beam parameters on voltage. It is
known that the form and mutual dispositions of the
cathode, anode and focusing electrode have the greatest
influences on electron trajectories.
2 METHOD OF SIMULATION
Geometry of electrodes is shown in Fig. 1. The error
∆1 arises during a cathode installation in a longitudinal
position and heating it.
4∆2
∆1
1 2
5
3
1400 1200 1000 800 600 400 200 0
Fig. 1. Gun with the replacing cathode and the temperature distribution in electrodes.
1 − anode (injector body), 2 − cathode, 3 − focusing electrode 4 − adjusting element, 5 − springing holders.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 134-136.
134
mailto:kushnir@kipt.kharkov.ua
Above is the simulation model and temperature scale in К.
The error ∆2 is connected with a gun installation on
the accelerator since the anode usually is the injector
body (see Fig. 1). This error arises also during the re-
ducing of the anode−cathode gap that is sometimes used
for the extension of the cathode lifetime.
The beam parameters simulation was made with the
EGUN code [3] with an account of electrons thermal
velocities. A criterion of simulation validity was the in-
dependence of the beam parameters on voltage and on
emission properties of the cathode.
A thermal problem was solved using the numerical
method. For the account of a radiation heat transfer, the
area of the problem was divided into segments. The heat
transfer equation with a boundary temperature or radia-
tion flux was solved in each segment. The radiation heat
transfer was accounted only between two nearby fields
using the known dependence [4]:
∑ −= ∗
j
jijijii TTq ),( 44
,, σεϕ
Where qi is the radiation flux density on the i seg-
ment with the surface area Fi, σ = 5.67⋅10−8 W/m2K, ϕi,j
-angular factors [3]:
ji
jji
ji
F
,
,
coscos
ρ
θθ
ϕ = ,
θi, θj - angles contained by ρi,j vector and normal vectors
ni, nj respectively.
ε∗i,j is generalized emissivity factor of a radiation:
)1/1()1/1(1
1
,,
, −+−+
=∗
jijiji
ji εϕεϕ
ε ,
Here εi,εj are emissivity factors of mutually irradiat-
ed surfaces.
The temperature Тj was updated by the method of it-
erations. The error of the calculation is evaluated by
magnitude ± 5 %. Such there was an average correction
to Тj after 4-5 iterations. The refinement of this result
can be reached by the increasing of a number of itera-
tions that however is deprived of a sense because of
large indeterminations in the emissivity factor of sur-
faces.
3 RESULTS AND DISCUSSIONS
As can been seen from Fig. 1, the difference be-
tween the cathode and enclosing electrode temperatures
is about 500 К. With account of the divergence between
expansion coefficients of various constructional materi-
als used in guns (∆λ∼7⋅10-6 К-1 between molybdenum
and stainless steels) and scale of details sizes (~ 10 mm)
it is possible to say that the temperature deformations
leading to a deviation from optimal geometry are less
than 0.05 mm.
Obviously the indicated error may be considerably
reduced by the choice of material and by the design of
electrodes. It is necessary to mark, that the necessary in-
creasing of a emission density in going to small-sized
guns is satisfied usually by increasing of emission prop-
erties of the cathode instead of temperature ones. There-
fore relative temperature deformations will not been in-
creasing, that increases a role of the installation toler-
ance of electrodes. To estimate the acceptable tolerance
it is necessary to find criterions of beam parameters de-
viations.
The calculated values of perveance and emittance of
the beam for various positions of the anode and cathode
relatively to the focusing electrode are represented in
Fig. 2 and Fig. 3.
∆ R/R
∆ ε / ε
∆ P/P
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
∆ 1 , mm
Fig. 2. Relative variations of emittance − ∆ε/ε, per-
veance − ∆P/P and the beam radius−∆R/R vs the
anode displacement ∆1.
ε=30.3π⋅mm⋅mrad, µР=0.54, R=3mm.
The greatest deviations at small ∆1, ∆2, as can be
seen, are observed for the emittance. Let's consider that
the emittance of technological accelerators is limited by
the acceptance of a transport system only. In this case
[5]: ε = A and А = (2π2/λ)a2, where λ is a focussing pe-
riod, a is radius of the aperture, A − acceptance. The pa-
rameter λ is connected with a disposition of focusing el-
ements, therefore, λ = const. In this case the permissible
emittance oscillations are determined by the aperture
only. Then
∆ε/ε = 2∆а/a > 0.1-0.2,
where ∆а = а⋅(0.05 ÷ 0.1) is halo size of a beam.
∆ P/P
∆ ε / ε
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.1 0.2 0.3 0.4 0.5
∆ 2, mm
Fig. 3. Relative deviations of the emittance − ∆ε/ε
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 135-136.
135
and perveance − ∆P/P vs the cathode displace-
ment − ∆2.
As one can see from the indicated figures, the condi-
tion ∆ε/ε <0.2 corresponds to the tolerance ∆1, ∆2 ≤ ±
0.1 mm.
For X − band guns according to the scaling theory
[1] ∆1, ∆2 ≤ ±0.01 mm is necessary that is difficult to re-
alise in conditions of usual laboratories. The construc-
tions of the gun with an adjustment insertion 4 (see
Fig. 1) are interesting for overcoming these difficulties.
In connection with a problem of a high electric power
transfer to small-sized cathodes, arise a question of a
heat leak via such insertions.
As shown by numerical simulations and experimen-
tally, the operation temperature 1500К of the BaNi-
cathode in the design in Fig. 1 requires a heat power of
about 50 W, 30 W of them is dispersed by radiation.
The dominant role of radiation in the heat transfer al-
lows using such insertions for the reaching the cathode
tolerance installation ∆2 ≤ ±0.01 mm without significant
losses of heat.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 10 20 30 40 50 60
P, W
R
,
Ω
Fig. 4. A resistance of a heat wire of the BaNi-cath-
ode vs the input electric power.
ο − gun without insertion (4), • − with insertion.
For the heat transfer process studies two guns were
tried. One of them, having an adjusting insertion (4),
shown in Fig. 1. Such insertion with thickness of
0.3 mm was made of a stainless steel and with a roughly
surface for the reducing of the heat transfer via the end
face contacting with a focusing electrode (3). The resis-
tance of heating wire in the dependence on the cathode
temperature is shown in Fig. 4. One can see that temper-
ature of the cathode without the insertion is higher in the
field of low powers only, i.e. for low temperatures when
predominates a kinetic heat transfer instead of radiation
one. Both curves coincide in the field of high tempera-
tures. The dependence for the cathode with an insertion
has even the smaller derivation that apparently is con-
nected with a shielding from irradiation of a focusing
electrode by the insertion.
Going to compact high intensive electron sources re-
quires operating it nearby current saturation. A source
of beam parameter instabilities in this regime may be
the loss of emission as shown in Fig. 5.
R, mm
L, cm
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
1 1.5 2 2.5 3 3.5
I, A
Fig. 5. Position of crossover L and beam radius in
the crossover vs emission ability of cathode I.
Here I is the current of saturation for cathode with
the 1.54 cm2 emission area in the gun presented in
Fig. 1. As can be seen, for the emission abilities more
then 2.7 A indicated parameters are stable.
4 CONCLUSION
Thus, obtained results showed a possibility to create
the precision intensive thermionic electron sources with
replacing the cathode for the compact technological
linacs. Such sources must be supplied with the cathode
having an enough reserve of emission for conservation
of beam parameters unvaried in long time.
5 ACKNOWLEDGMENTS
This work was partially supported by STCU project
# 2185.
REFERENCES
1. J.R.Pierce. Theory and design of electron beams.
New York, 1954, 214 p.
2. V.V.Bulanova, G.P.Egorov, Ya.I.Mestechkin.
Comparison of experimental research and account
on the computer of an electron-optical system //
Electronic engineering. A series 1. Microwave
electronics. 1973, № 7, p. 58-69.
3. W.B.Herrmannsfeld. EGUN: Electron Optics Pro-
gram, Stanford Linear Accelerator Center, SLAC-
PUB-6729, 1994.
4. S.N.Shorin. Heat transfer. Moscow: Higher school,
1964, 489 p. (in Russian).
5. A.N.Lebedev, A.V.Shal'nov. A fundamentals
physics and engineering of accelerators. Moscow:
Energoatomizdat, 1991, 528 p. (in Russian).
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 136-136.
136
|
| id | nasplib_isofts_kiev_ua-123456789-79021 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-02T06:36:51Z |
| publishDate | 2001 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Khodak, I.V. Kushnir, V.A. Mitrochenko, V.V. Stepin, D.L. Zhiglo, V.F. 2015-03-24T17:46:33Z 2015-03-24T17:46:33Z 2001 Thermal effects and beam parameter variations in electron guns / I.V. Khodak, V.A. Kushnir, V.V. Mitrochenko, D.L. Stepin, V.F. Zhiglo // Вопросы атомной науки и техники. — 2001. — № 5. — С. 134-136. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS numbers: 29.25.Bx, 41.85.Ar https://nasplib.isofts.kiev.ua/handle/123456789/79021 The paper describes results of research on influence of electrode temperatures and manufacturing tolerance of an electron gun on parameters of an output beam. The Pierce's gun that provides an electron beam with a current of 1.2 A and energy of 25 keV for the S-band technological linac is considered as an example. Numerically calculated parameters of the beam and the temperature distribution in electrodes are presented. It is shown that the acceptable error in a position of electrodes is ±0.1 mm. This value does not fall outside the limit of thermal deformations and technical abilities for manufacturing guns in a laboratory. The scaling to the area of injectors for compact X-band linacs leads to the tolerance of ±0.01 mm that requires introducing fixing and adjustment elements reducing a thermal insulation of the cathode. However, the calculation and experiment showed that such reducing is negligible even for the modern low temperature thermionic cathodes due to a dominant role of the radiation in the heat transfer. This circumstance permits to create the precision intensive compact thermionic electron sources with replacing cathode for the compact linacs. This work was partially supported by STCU project # 2185. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Thermal effects and beam parameter variations in electron guns Температурные эффекты и изменения параметров пучка в электронных пушках Article published earlier |
| spellingShingle | Thermal effects and beam parameter variations in electron guns Khodak, I.V. Kushnir, V.A. Mitrochenko, V.V. Stepin, D.L. Zhiglo, V.F. |
| title | Thermal effects and beam parameter variations in electron guns |
| title_alt | Температурные эффекты и изменения параметров пучка в электронных пушках |
| title_full | Thermal effects and beam parameter variations in electron guns |
| title_fullStr | Thermal effects and beam parameter variations in electron guns |
| title_full_unstemmed | Thermal effects and beam parameter variations in electron guns |
| title_short | Thermal effects and beam parameter variations in electron guns |
| title_sort | thermal effects and beam parameter variations in electron guns |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79021 |
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