Optimization of the driving circuit for material processing with a pulsed-glow discharge

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 3, JUNE 2000 1035

Optimization of the Driving Circuit for MaterialProcessing with a Pulsed-Glow Discharge

Yanina Cesa, Nélida Mingolo, and Oscar Eduardo Martínez

Abstract—The effect of including an inductance in the circuitof a glow-discharge-pulsed electron gun for materials processingis analyzed. Due to the particular nonlinear behavior of the cur-rent vs voltage in these guns, and the strong nonlinear self-focusingof the beam, the adequate shaping of the temporal profile of thedischarge becomes relevant to the efficiency of the system. A crit-ical damping value for the inductance is obtained and within therange of practical interest, analytical expressions are derived forthe required inductance, capacitance and source voltage for a givenpeak power, pulse duration, gas pressure, and pulse shape. The ef-ficiency increase with the improved design is also discussed.

Index Terms—Electron gun, glow discharge, surface treatment.

I. INTRODUCTION

M ETALLIC SURFACES treatment can be accomplishedby means of energetic beams [1]–[5], and a different

procedure, which is the use of laser surface melting for changingthe structure of a layer of the material by solidification afterrapid cooling toward the substrate [6]–[13]. Alternatively,continuous-wave (CW) electron beams (-beams) have beenused for annealing purposes [14]–[17]. Single-shot surfaceamorphization of a well-known glass-forming alloy has beenpossible by means of energetic-beam pulses generated by coldcathode-glow discharges [18]. For this technique, in previouswork, Mingolo et al. used a modified version of a flat-cathodeelectron gun originally designed for plasma excitation [19].These e-beams had energies in tens of kilovolts (kV), andcurrents of tens of amperes. Besides their simplicity and lowcost, the other potential advantages of this type of guns forsurface treatment include the easily obtainable large energy pershot [tens of Joules (J)], the lower reflectivity and the largerpenetration of the electrons in metals as compared to light, anda depth profile that does not peak at the surface [20], [21].

A careful analysis of the self-focusing action of the beam dueto the magnetic force created by the beam itself indicated a hugesensitivity of the location of the focus with the beam current.Several modifications were introduced to the original design inorder to improve the shot-to-shot reproducibility [22] and the

Manuscript received December 2, 1999; revised March 20, 2000. This workwas supported in part by the Universidad de Buenos Aires, CONICET and theAgencia Nacional de Promoción Científica y Tecnológica.

Y. Cesa and N. Mingolo are with the Laboratorio de Haces Dirigidos, Depar-tamento de Física, Facultad de Ingeniería, Universidad de Buenos Aires, PaseoColón 850, 1063 Buenos Aires, Argentina.

O. E. Martínez is with the Laboratorio de Electrónica Cuántica, Departamentode Física, Facultad de Ciencias Exactas y Naturales, Universidad de BuenosAires, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina.

Publisher Item Identifier S 0093-3813(00)05705-2.

energy deposition efficiency by using a curved cathode with re-duced sensitivity of the focal point with current [23].

Despite the previous improvements, the rapid change of thefocal point with the current rapidly broadens the beam area re-ducing the energy density deposited in the sample. In this paper,the temporal pulse shape is modified by means of an induc-tance included in the discharge circuit in order to avoid the rapidchanges in the current, rounding the shape of the current pulse,and hence, delaying the defocusing action improving the effi-ciency of the system. The use of an inductance in order to shapecurrent pulses in discharge circuits has been implemented be-fore [24]–[26] in the design of flashlamp discharge circuits forlaser pumping. In our system, not only the phenomenologicalnonlinear equations are different, but also the motivations, opti-mization, and design criteria. It will be shown that the inclusionof the inductance results in an increase in the energy-depositionefficiency in the treated material, and additionally has the ben-eficial property of reducing the probability of arc development.

In Section II the nonlinear impedance of the gun is charac-terized experimentally and fit with a phenomenological expres-sion. The numerical simulation of the discharge is carried out inSection III, and the design equations are derived in Section IV.The energy-deposition efficiency increase is discussed in Sec-tion V, and finally, the conclusions are presented in Section VI.

II. DISCHARGECIRCUIT

The electron gun is a modified version of the one presentedpreviously [22], [23]. It consists basically of a concave alu-minum cathode 75 mm in diameter and with a radius of curva-ture of 200 mm. The cathode is placed inside a low-pressure gaschamber. Helium gas was flown through the chamber, creating apressure of 40 Pa for the generation of the high-voltage glow dis-charge. A small partial pressure of Owas also used to maintaina thin oxide layer on the aluminum cathode surface. Without thisoxygen flow, the removal of the oxide layer by sputtering afterrepetitive firing of the discharge significantly decreases peakcurrent due to a reduction in the cathode’s electron yield. Thecathode is connected to a negative high-voltage power supply.The discharge circuit and a typical ; curves measuredwith a voltage probe and a Rogowsky coil are shown in Fig. 1(a)and (b), respectively. Before triggering the circuit, the powersupply charges the capacitorto a voltage . When the sparkgap ( ) is triggered, the glow discharge evolves. In the absenceof the inductance, the current is established by the resistorand the current vs voltage characteristic of the discharge [27].Typical values used previously are .

0093–3813/00$10.00 © 2000 IEEE

1036 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 3, JUNE 2000

(a)

(b)

Fig. 1. (a) Schematic diagram of the electron gun and discharge circuit. The “keep alive” current is kept throughR , and the main discharge of capacitorC isset by the triggerT , through a limiting resistorR and the inductanceL = 660 �H added in this paper. A Rogowski coil (RC) and a high-voltage probe (HVP)monitor the discharge. (b) Typical beam current and cathode voltage pulse measurement

In prior works [19], [22], it was assumed that the relationbetween the beam current and the cathode-sample voltagedrop was given by

(1)

where the parameter depends on the gas pressure, degree ofoxidation of the cathode, and it was determined, together with

the exponent , using the peak values of the current and voltage,that yielded A/(kV) and .

We have detected a small delay between the peak current andthe peak voltage, and found a better model for the discharge byfitting the entire curve. Least-square fits of the plotversus were made for different shots at different ini-tial voltages and for a constant gas pressure of 38.66 Pa of Heand 1.33 Pa of O. The results yielded and the

CESAet al.: OPTIMIZATION OF THE DRIVING CIRCUIT 1037

Fig. 2. Empirical fit of the current–voltage characteristic of the discharge. Forthis particular case, the source voltage wasV = 18 kV and the chamberpressure 40 Pa. The experimental data were fit toi = aV yielding k =

3:5 � 0:1 anda = 1:5 � 10 A/(kV) .

parameter fluctuated between A/(kV) andA/(kV) , depending on the oxidation cathode condition. Thisfluctuation is reduced after several shots obtaining repetitive re-sults indicating that the cathode reaches a stable regime. Nev-ertheless, it is useful to notice that the value of the exponentis not sensitive to such situation. In Fig. 2, a typical plot is pre-sented, which shows the quality of the fit.

III. N UMERICAL COMPUTATION OF THEDISCHARGE

Using the phenomenological electrical response for the elec-tron gun given by (1), the circuit shown in Fig. 1(a) responds tothe differential equations:

(2a)

(2b)

whereis the capacitor charge,is the capacity, andis the sum of the ballast resistor , and the inductanceresistance is .

Using dimensionless variables as follows:

(3a)

(3b)

(3c)

(3d)

(3e)

(3f)

(3g)

where is the source voltage, and

(3h)

Equation (2) can be written as

(4a)

(4b)

In order to simplify the reading, a summary of the symbolsused in the text is presented in Table I.

These equations were numerically computed and the resultsfor and were compared with the experimental resultsfor the following conditions: H, nF, and

. The chamber pressure was 40 Pa andkV. The parameter was adjusted in order to recover the samepeak values. The comparison between the simulations and ex-perimental results are shown in Fig. 3.

An excellent accordance between the experimental resultsand the numerical predictions is observed, gaining confidencein the conclusions that will be driven from the numerical simu-lations that follow. The simulations will be performed assuming

(i.e., negligible resistance as compared to the inductanceand gun impedance), the validity of such an approach will bejustified later.

The only parameter left in the dimensionless equation (4) is, that was scanned between 0.01 and 10. The solution for

presented a critical damping for , and oscillations forlarger values of the parameter. These oscillations are an artifactof the equations, as the real gun is not symmetric and cannotinvert the current, so that we stop the simulations when the cur-rent changes sign. In Fig. 4(a), the results for and arepresented for and . The simulations wereperformed keeping for all cases the same peak value for the cur-rent ( ), for the voltage ( ) and the same initially stored energyin the capacitor.

The numerical simulations show that asis increased, thecurrent and voltage peaks become more rounded and broaden,as shown in Fig. 4(a). The current pulse full-width at half max-imum (FWHM) increases from s for to sfor . As the critical value for is approached, the pulseshape becomes less sensitive to this parameter, and no substan-tial differences appear between and . For thelower values of , the current and voltage pulses present longtails that carry a large portion of the energy of the pulse. As thebeam defocuses when the current decreases, these long tails im-pinge in the sample in a broad area, which results in a loss ofenergy density-deposition efficiency.

This fact is shown in the simulations of the beam radius atthe sample and power density (Vi/area) presented in Fig. 4(b)and computed following [22]. For the simulations, the cathodesample distance was set such that the minimum radius resulted1.5 mm. The rounded current pulses for larger values ofyield abeam focused during a longer period of time. This fact results ina broader intensity (power density) pulse and, hence, in a moreefficient energy deposition in the sample. In fact, the intensity


TABLE ISUMMARY OF THE SYMBOLS USED

Fig. 3. Plot of the experimental and numerical results for the cathode voltage and the beam current. For the numerical simulationsa = 1:5 � 10 A/kV wasused in order to fit the peak values for the current and voltage. The circuit parameters were:L = 660 �H,C = 100 nF, andR = 39 .

pulsewidth (FWHM) increases from s for tos for . From to the critical value ,

the pulse broadens only another s. At larger values of the

parameter , the voltage in the capacitor is inverted, and thereis a loss in efficiency due to this remnant energy stored after(with inverted voltage) the current switches off.


(a)

(b)

Fig. 4. (a) Numerical simulations of the current and cathode voltage performed for different values of the damping parameter�, for � = 0. For all cases the samevalues for the stored energy and peak current were used. (b) Numerical simulations of the beam radius and power density at the sample. The sample was located15.2 cm away from the cathode of 20 cm radius of curvature (following the model presented in [22] and [23]). The simulations correspond to the same casesasin (a).

IV. DESIGN EQUATIONS

In a practical situation in which one desires to design a dis-charge circuit for a gun for material treatment, one should fixthe desired peak value and duration for the power pulse. Theparameter should be set to the critical value 8.5, but to our ex-perience, this gives rise to large inductance and source voltages.Hence, we decided to leaveas a free parameter for the design.The design equations should provide the value for , and .

The dimensionless current reaches a peak value that dependson the parameter, as shown in Fig. 5. In the region of practicalinterest between and , the curve can be fit by

(5)

with , , and .In a similar manner the FWHM of the power pulse ( )

was computed as a function of the parameter. In this case, anexcellent fit was found for

(6)

as shown in Fig. 6.Using the numerical fits given by (5) and (6), and the defini-

tions of the dimensionless variables (3), the values of and

Fig. 5. Plot of the peak dimensionless currenty as a function of the parameter�. For the range of interest, the numerical result was fitted byy = A +B ln(�) + C[ln(�)] , withA = 0:32,B = �0:098, andC = 9:67 � 10 .This fitting parabola is also plotted in the figure (solid line).

can be obtained from the selected values for the peak power, the power FWHM , and the parameter, provided that

the gun parameter is known:

(7)


TABLE IIDESIGN PARAMETERS FORDIFFERENT VALUES OF THE DAMPING PARAMETER �, FOR FWHM OF THE POWER PULSE T = 18 �s

AND PEAK POWERP = 500 kW

Fig. 6. Plot of the dimensionless FWHM of the power of the pulse� =g(�). The function is approximated byg(�) = 2� . This approximationis shown in the plot (full line).

(8)

(9)

Additionally, the following values can be determined for thestored energy and the peak current and voltage:

(10)

(11)

(12)

The design equations obtained are valid provided that the re-sistance has a negligible effect in the discharge ( ). Theratio between the energy dissipated in the resistorand theenergy stored in the capacitor can be estimated as

(13)

and results proportional to the peak voltage drop in the resistor. The term grows with , and is of the order

of one for critical damping. For typical values for the currentof about 30 A and , less than 5% of the energy isdissipated in the resistor and justifies the approximationused.

As an example, the solutions for three different damping pa-rameters are shown in Table II, where we have set as designingconditions a peak power of 500 kW, s, and

A/kV (similar to those used in our experiments for

steel treatment, and corresponds to the case shown in Fig. 3).The parameter corresponds to the case of Fig. 3.The values in the table were calculated using (7)–(9). The lastcolumn corresponds to the efficiency obtained by dividing theproduct by the stored energy, and is discussed in theSection V. It is evident that less stored energy is needed for thesame peak power and pulsewidth in the case of critical damping.Nevertheless, the values for the source voltage increases signifi-cantly. In order to reduce the inductance and the source voltage,one can compromise with the damping parameter setting ,which still yields a reasonable efficiency. This shows the conve-nience of leaving as a free parameter in order to compromisethe design with more practical values.

V. ENERGY-DEPOSITIONEFFICIENCY

Due to the defocusing of the beam as the current drops, thebeam area at the sample increases and the energy-deposition ef-ficiency decreases. The optimal design corresponds to a criticaldamping, which yields the most rounded shape (smaller secondderivative), which keeps the beam focused for a longer periodof time. If one compromises the design reducing the value ofthe damping parameter, one should verify that the efficiencydoes not drop substantially.

The sensitivity of the focusing with the current depends onhow tightly the beam is focused initially [22], [23]. One can as-sume approximately that once the peak power decreases beyonda factor (that will depend on the particular location selected forthe sample), the beam is defocused and does not provide addi-tional useful energy. Hence, one should estimate how much en-ergy is deposited while the discharge is above. Calling suchenergy and approximating the pulse shape by a parabolawith peak power and FWHM , one obtains

(14)

The energy deposition efficiency can then be defined as:

(15)

where (3), (10)–(12), and (14) were used. The coefficientisthe contribution to the total efficiency due to the damping con-ditions, while the term depending onis relate to the particularfocusing selected for the sample.

The coefficient is plotted in Fig. 7, showing the increasein efficiency as the critical value is approached (where ).


Fig. 7. Plot of the efficiency parameter" that indicates the relative energydeposition efficiency as compared to that at critical damping. For small valuesof � a logarithmic behavior is observed as shown in the inset. For� above 1,the improvement is very small.

The values plotted in the figure correspond to those obtainedfrom the numerical simulation of the discharge for each valueof and show numerical errors originated in the determinationof the pulsewidth. The values obtained with the approximateformula given by (5) and (6) yield numbers with less than 2%error. Notice that for the previous example in which wasselected, the efficiency decreases to 92%, while the damping pa-rameter used in our experiments yield an importantloss in the efficiency. The low sensitivity of the efficiency with

near the critical damping allows the mentioned compromisein the design. Larger departures from the critical damping com-promises more seriously the efficiency, that has a logarithmicdependence for (see inset in the Fig. 7).

VI. CONCLUSION

Provided that the beam focusing on the glow-discharge elec-tron gun used for materials treatment is very sensitive to thevalue of the current, it is convenient to design the discharge cir-cuit in such a manner as to obtain a temporal dependence of thecurrent as rounded as possible. With this purpose in mind, aninductance was added to the discharge circuit and the charac-teristic nonlinear impedance of the gun was measured and fittedsemiempirically. With this result, a dimensionless equation forthe temporal evolution of the discharge was written, dependingonly in two parameters and . One of them, ( ), was shownto be negligible at typical operating conditions.

From the numerical simulations, it was shown that there is anoptimum value for the parameter, for which critical dampingis obtained, providing a more-rounded pulse and more-efficientenergy deposition in the sample. The critical value was

, but it was shown that for values of the parameter as low as, the loss in efficiency is relatively low, and less restrictive

design conditions are met.Design equations were derived for the discharge circuit that

provide the values for the inductance, capacitance and sourcevoltage necessary for given values for the peak power, pulseduration, and damping parameter.

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Yanina Cesareceived the Licenciada en Física (M.S.) degree from Universidadde Buenos Aires, Argentina, in 1998. She is currently working toward the Ph.D.degree from the same university in the area of phase transitions characterizationtechniques.

Nélida Mingolo received the Licenciado en Física (M.S.) and the Ph.D. degreesin physics from the Universidad de Buenos Aires, Argentina, in 1981 and 1992,respectively.

She has worked mainly on amorphous metals and fast-quenching techniques,as well as characterization techniques for metastable phases. She is currently aProfessor at the Universidad de Buenos Aires and head of the Directed BeamLaboratory, where the electron beam treatment of metallic surfaces is being de-veloped.

Oscar Eduardo Martínez received the Computador Científico, the Licenciadoen Física (M.S.), and the Ph.D. degrees in physics from Universidad de BuenosAires, Argentina, in 1975, 1976, and 1982, respectively.

He is currently a Full Professor at the Universidad de Buenos Aires andMember of Research Staff of Consejo Nacional de Investigaciones Científicas yTecnológicas de la República Argentina. He has published more than 60 papers,mainly on ultrashort pulse generation.

Dr. Martínez is a Fellow of the Optical Society of America.

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Optimization of the driving circuit for material processing with a pulsed-glow discharge