268 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 1, FEBRUARY 2000

On the Delay Time for the Onset of RadiographicSpot Size Growth

Thomas J. T. Kwan

Abstract—We have revisited the physical mechanisms, whichlead to a time delay of the onset of the undesirable spot size growthin high-dose X-ray radiography. In our theoretical model, the delaytime is partially due to the time needed for the electron beam tothermally ionize the target spot resulting in target ions and par-tially due to the time needed for the ions to form a column of at leasta quarter of the betatron wavelength of the electron beam. Basedon our model, an analytic formula is derived, and it has been foundto be consistent with experimental observations for different targetmaterials and beam parameters. Our analysis shows that the delaytime is directly proportional to the beam spot size at the target andinversely proportional to the beam current. Our calculations fur-ther show the spot size of the DARHT-1 beam with 2 kA currentshould be stable because the delay time of about 69 ns is longerthan the beam pulse length.

Index Terms—Beam-target interaction, electron beam spot, ionneutralization, radiography.

I. PHYSICAL MODEL

I IN HIGH-DOSE X-ray radiography, the electron beam en-ergy density deposited on the target can vaporize the target

spot during the beam pulse. The temperature of the target fluidcan range from a fraction to tens of electron volts. If the tem-perature is on the order of an electron volt, the target plasmais almost fully ionized. Further increase in temperature can in-crease the presence of multiply ionized ions and thereby the av-erage ionization, , can be greater than unity. The minimumtime for significant ionization to occur at the target spot afterthe incidence of the electron beam is determined by the thermalenergy needed to cause ionization of the target material. Onceionization occurs, the ions will travel upstream toward the elec-tron beam. They then cause partial charge neutralization of theelectron beam, but insignificant current neutralization becauseof their very low velocity. As a result, the electron beam un-dergoes self-pinching because of the dominance of its magneticforce. For highly relativistic electron beams, pinching can occurwith small fractional charge neutralization. [1] The focal lengthof the pinch is equal to the quarter wavelength of the betatronmotion [2] of the electron beam, and it is given by

(1)

Manuscript received April 22, 1999; revised July 26, 1999. This work wassupported by the U.S. Department of Energy.

The author is with the Plasma Physics Applications Group, Applied Theo-retical and Computational Physics Division, Los Alamos National Laboratory,Los Alamos, NM 87544 USA.

Publisher Item Identifier S 0093-3813(00)00743-8.

whereradius;current;relativistic factor of the electron beam;fractional neutralization.

The parameter is defined by in cgs units, andits convenient numerical value is 17 kA. After ionization startsto happen at the target, the beam spot will decrease in time asthe ions move out to increase the axial length of the neutralizingcolumn. The minimum beam spot occurs at the time when theion column is equal to a quarter of the betatron wavelength. Asthe ion column continues to grow in length, the electron beamspot on the target will start to increase in proportion to the ioncolumn. The temporal rate of increase is approximately linearlydependent on the ion velocity.

II. A NALYSIS

Our hydrodynamic calculations indicate that average ioniza-tion, , of the target material such as tantalum, tungsten, andcopper, becomes significant when the target material reaches itsvaporization point. The time for the target spot to reach such anionization state depends on the energy density deposition by theelectron beam, the specific heat, and the vaporization tempera-ture of the target material. The latent heat for phase change fromsolid to liquid is only a few percent of the energy needed in theprocess, and hence has been neglected in our analysis. The timeto reach vaporization temperature is given by [3]

(2)

wherespecific heat of the target material;specific boiling temperature of the target material;area of beam spot on the target;electron charge;beam current;energy loss of incident electrons in the target in unitsof eVcm2/g.

The velocity of the ions can be calculated in the following. Asthe ions are generated, they are accelerated by the space chargepotential of the electron beam. Their streaming velocity is thengiven by

(3)

0093–3813/00$10.00 © 2000 IEEE

KWAN: ON THE DELAY TIME FOR THE ONSET OF RADIOGRAPHIC SPOT SIZE GROWTH 269

whereaverage ionization of the ions;space charge potential;mass of the ions.

The time for the ions to travel a distance of a quarter betatronwavelength is given by . From (1) and (3), we have

(4)

For an infinitely long solid beam of radius in a metallic tubeof radius with a strong axial magnetic field, the space chargepotential on axis is [4]

(5)

where and is the relativistic factor of theelectron beam. Substituting (5) into (4), we obtain the time forthe ions to form such a channel,

(6)

We note the important parameter dependence thatis directlyproportional to the radius of the electron beam and inverselyproportional to its current.

The time for the onset of the growth of the spot size is thengiven by

(7)

Some important conclusions can be drawn from (7). To maxi-mize the delay, the target material should have high vaporiza-tion temperature, high specific heat, and large atomic number,and the electron beam should have low current, high energy, andlarge radius. We further notice that not all the desirable parame-ters are suitable for high-dose radiography applications. There-fore, one can use (7) for system optimization studies to arrive ata set of parameters for a particular facility.

III. EXPERIMENTAL VALIDATION

Target experiments had been carried out at the Integrated TestStand (ITS) of the DARHT facility at Los Alamos NationalLaboratory [5] and the ETA-II facility at Lawrence LivermoreNational Laboratory [6]. The analysis of the ITS experimentsshowed that the growth of the spot size was consistent with

the presence of ions from target materials [3], [5]. The exper-imental observations do not support the hypothesis [1] of ionemission due to target surface contaminants and desorption ofmonolayers. The delay time for the onset of spot size growth wasexperimentally observed to be 40 ns for a copper target and 60ns for a tantalum target. In the target experiments, the electronbeam had an energy of 5.6 MV and current 3.0 kA with coppertarget whereas 1.5 kA with the tantalum target. The beam had aspot of approximately 0.15 cm in radius on the target plane. Thetarget plane was 2.0 cm from the collimator separated by a driftspace with a wall radius about 17 cm. Because of the two-di-mensional (2-D) nature of the target chamber, the space chargepotential of the electron beam in the experiments can only beaccurately determined by 2–D particle-in-cell simulation. Oursimulation results indicated the average ion energy was about350 keV for the copper experiment and about 200 keV for thetantalum experiment. The charge neutralization factor(radi-ally integrated across the electron beam) is found from our simu-lations to be about 0.2 at the midpoint of the ion column. For thecopper target, (2) gives 14 ns, and (4) gives 29 ns. The calculateddelay is 43 ns, which compares very well with the experimentalresult [3]. For the tantalum target, (2) gives 22 ns, and (4) gives46 ns. The calculated delay is 68 ns, which is consistent withthe experimental value of 60 ns [3]. As for the experiments atETA-II with tantalum targets and an electron beam pulse of only40 ns, our analysis indicates that the beam pulse is too short toobserve any growth of the beam spot. Our conclusion is consis-tent with the ETA-II experimental results.

IV. I MPLICATION ON DARHT-1 BEAM

The DARHT-1 beam, which is expected to be operational inJuly 1999, will have energy of 20 MV and current of 2.0 kA.Eventually, its current is anticipated to reach the design value of4.0 kA. The drift tube radius is 5.0 cm, andis estimated to be0.2. For 2.0 kA current and a spot size of 2.0-mm on a tantalumtarget, (7) yields a delay time ns nsns. Since the main electron beam pulse is designed to be 60 ns,we expect the beam spot will not be adversely affected by thepresence of tantalum ions. On the contrary, the spot size willdecrease during the pulse due to a gradual pinch caused by theions. This effect can provide a tighter spot size advantageous forthe resolution of the radiographic system. On the other hand,if the electron beam has a smaller spot size such as 1.0 mmand higher beam current of 4.0 kA, the delay time will only be

ns ns ns. Therefore, we would expectthat the spot size of the DARHT-1 beam operated at these morestringent parameters will start to growth after approximate 15ns into the pulse. In this case, a self-bias target can be an optionto mitigate this undesirable effect [3], [5], [7].

V. CONCLUSION

Our theoretical model on the onset of the growth of thebeam spot due to ion emission from the target has resulted inan analytic expression, which depends on the beam parameterssuch as voltage, current, spot size, and geometric effects ofthe target chamber. This model is found to be consistent withexperimental observations from the ITS experiments at Los

270 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 1, FEBRUARY 2000

Alamos and ETA-II experiments at Livermore. Our analysisfurther predicts that the DARHT-1 beam will not suffer fromthe spot growth due to target ions if it is operated at 20 MV en-ergy, 2.0 kA current, and with a spot size of 2.0 mm. However,with 4.0 kA and a spot size of 1.0 mm, we show that the beamspot will start to increase after about 15 ns into the beam pulse.Consequently, a mitigating method, such as the self-bias target,is needed to stabilize the spot size.

ACKNOWLEDGMENT

The author wishes to express his appreciation to L. Le Dainfor raising some stimulating questions, which lead to this anal-ysis. The author would like to thank Y. J. Chen, D. Moir, S.Sampayan, and C. Snell for many valuable discussions.

REFERENCES

[1] D. R. Welch and T. P. Huges, “Effect of target-emitted ions on the focalspot of an intense electron beam,”Laser Part. Beams, vol. 16, no. 2, pp.285–294, 1998.

[2] S. Humphries Jr.,Charge Particle Beams. New York: Wiley, 1990.[3] “Physics of Plasmas,” Los Alamos National Laboratory, LA-UR-98-

4802, 1998 (AUTHOR: UPDATE?), submitted for publication.[4] R. B. Miller, An Introduction to the Physics of Intense Charged Particle

Beams. New York: Plenum, 1982.

[5] T. J. T. Kwan, D. C. Moir, B. G. DeVolder, C. M. Snell, and M. Kang,“Design simulation for spot size stabilization of ITS/DARHT,” inProc.XIX LINAC Conf.. Chicago, IL, Aug. 23–28, 1998, pp. 660–662.

[6] S. Sampayan, G. Caporaso, Y.-J. Chen, C. Crist, M. Garcia, T. Houck,M. Krogh, R. Richardson, J. Weir, and G. Westenskow, “Experimentalinvestigation of beam optics issues at the Bremsstrahlung converters forradiographic applications,” inProc. XIX LINAC Conf. Chicago, IL, Aug.23–28, 1998, pp. 314–316.

[7] T. J. T. Kwan and C. M. Snell, “Electron beam spot size stabilizationfor radiographic applications,” inProc. 1998 Int. Congress on PlasmaPhysics, vol. 22C, P. Pavlo, Ed. Prague, Czech Republic, July 1998.

Thomas J. T. Kwan received the Ph.D. degree inphysics in 1978 from the University of California,Los Angeles.

His field of specialization is theoretical andcomputational plasma physics. He has been withthe Los Alamos National Laboratory, Los Alamos,NM, since 1978, and is currently a Staff Memberin the Plasma Physics Applications group. His areasof research have included particle-in-cell simulationof plasmas and its incorporation of Monte Carlocharged particle transport, free-electron lasers,

intense charged particle beam theory, and high-power microwave generation,propagation, and target interaction. One of his current research interests isintense electron-beam driven flash X-ray radiography.