Focal waveforms for various source waveforms driving a prolate-spheroidal impulse radiating antenna (IRA)

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1 RADIO SCIENCE, VOL. 43,, doi: /2007rs003775, 2008 Focal waveforms for various source waveforms driving a rolate-sheroidal imulse radiating antenna (IRA) Serhat Altunc, 1 Carl E. Baum, 1 Christos G. Christodoulou, 1 Edl Schamiloglu, 1 and C. Jerald Buchenauer 1 Received 15 November 2007; revised 23 January 2008; acceted 20 February 2008; ublished 26 Aril [1] Imulse radiating antennas (IRAs) are designed to radiate very fast ulses in a narrow beam with low disersion and high field amlitude. For this reason they have been used in a variety of alications. IRAs have been develoed for use in the transient far-field region using arabolic reflectors. However, in this aer we focus in the near field region and develo the field waveform at the second focus of a rolate-sheroidal IRA. Certain skin cancers can be killed by the alication of a high-amlitude electric field ulse. This can be accomlished by either inserting electrodes near the skin cancer or by alying fast, high-electric field ulses without direct contact. We investigate a new manifestation of an IRA, in which we use a rolate sheroid as a reflector instead of a arabolic reflector and focus in the near-field region instead of the far-field region. This technique minimizes skin damage associated with inserting electrodes near the tumor. Analytical and exerimental behaviors for the focal waveforms of two and four-feed arm rolate-sheroidal IRAs are exlored. With aroriate choice of the driving waveform we maximize the imulse field at the second focus. The focal waveform of a rolatesheroidal IRA has been exlained theoretically and verified exerimentally. Citation: Altunc, S., C. E. Baum, C. G. Christodoulou, E. Schamiloglu, and C. J. Buchenauer (2008), Focal waveforms for various source waveforms driving a rolate-sheroidal imulse radiating antenna (IRA), Radio Sci., 43,, doi: /2007rs Introduction [2] Fast high-amlitude electric field ulses can be used to kill skin cancer [Schoenbach et al., 2006]. This has been demonstrated by the insertion of electrodes near the tumor. Our motivation in this aer is to aly fast, high-electric field ulses without direct contact for the ossibility of killing skin cancer. Here we concentrate on the electromagnetic, rather than the biological asects of the roblem. [3] This aer is an extension of a revious aer [Baum, 2007]. IRAs have been develoed for radiating in the transient far-field region [Baum et al., 1999]. Related exerimental and numerical asects of this roblem can be found in Tyo and Buchenauer [2002] and Kim and Scott [2003]. In this aer we use a rolate sheroid as a reflector, launching an inhomogeneous lane wave from 1 Deartment of Electrical and Comuter Engineering, University of New Mexico, Albuquerque, New Mexico, USA. Coyright 2008 by the American Geohysical Union /08/2007RS one focal oint and reflecting it toward the second focal oint. 2. Descrition of Geometry [4] We choose a secial case of the rolate-sheroidal IRA s geometric arameters as in Baum [2007] and it is illustrated in Figure 1, where the geometric arameters are z ¼ z coordinate of the truncation lane a; b ¼ two radii for the rolate sheroid z 0 ¼ a 2 b 2 1=2focal distance ¼ a þ z 0 distance can be used for normalization Y ¼ radial coordinate ð1þ For our secial case in Baum [2007] and Altunc and Baum [2006a, 2006b], we have for the resent calculations z ¼ 0; a ¼ :625 m; b ¼ Y 0 ¼ :5 m; z 0 ¼ :375 m; ¼ 1m: ð2þ 1of9

2 [Baretela and Tyo, 2003] and it was easy to construct this version. Figure 1. IRA. Schematic diagram of a rolate-sheroidal Our design uses either two or four TEM feed arms. The dimensions of these feed arms are determined by 400 W and 200 W ulse imedances (f 0 =90, 60 ). In Baum [2007] the focal fields are calculated for a two-tem feedarm rolate sheroidal IRA. However, the analytical results can be simly extended to the four-arm case [Baum et al., 2004; Baretela and Tyo, 2003]. Figure 2 shows the TEM feed-arms geometry. [5] We have an increase of in the fields using the 60 TEM-feed-arm case as comared with the two-arm case [Altunc and Baum, 2006b]. In our design we used 60 feed-arm because the voltage gain is nearly maximum 3. Analytical Focal Waveform Calculations for Ste Excitation [6] The analytical focal fields were calculated in Baum [2007] and they are summarized here as 2 E d ¼ V " # 0 a þ z 0 q c Y 2 1=2 cot þ f g c a z 0 2 z 0 z E s ¼ V 0 2f g 1 z 0 z a þ z 0 E ¼ V 0 tan q c 2f g z 0 2 cot a z 0 ; q c 2 3 5; " 1 þ z # 0 z 2 1 ; Y E 2 ¼ V 0 1 b h 1 þ z i ; 2f g z 0 a þ z 0 b tan q c ¼ a þ z 1=2 a þ z 0 2 a z b ¼ 1 h Y 2 Y þ z i 2 1=2 z þ z o þ z o Y ðrevious resultþ; ð3þ where E d and E s are the imulse and ste terms from the reflection from the rolate shere and E is the magnitude of the reulse wave from first focus (valid u to the time of aerture truncation). The detailed calculations for tan(q c /2) are resented in Altunc and Baum [2006a] which is a simler result comared with the result in Baum Figure 2. Prolate-sheroidal IRA feed-arm geometry for four-arm case. 2of9

3 Figure 3. Analytic focal waveforms at the second focus (a) two feed-arm and (b) 60 four feedarm rolate-sheroidal IRA. [2007]. E 2 is the reulse term after the imulse (not included in Baum [2007] and is discussed in detail in Aendix A), q c is the angle of the feed arms with resect to the negative z axis, c is the seed of light in free sace, and f g is the transmission-line arameter f g ¼ Z c =Z 0 ; ð4þ where Z c and Z 0 are the transmission line and medium wave imedances, resectively. The analytical focal waveforms for a ram rising ste excitation are from Altunc and Baum [2006a]. The excitation is a 1 Volt (V 0 =.5 Volt) ste, rising as a ram function lasting 100 s. [7] We take the simle examle case in (1) to illustrate the analytical waveform. One can calculate the analytical focal fields of a two-arm rolate-sheroidal IRA from (3) as E ¼ 0:4 V=mðnegative reulseþ; E i ¼ E d ¼ 4V=m; t d E s ¼ 0:26 V=m; E 2 ¼ 0:06 V=mðnegative reulseþ: ð5þ t d is the risetime of the ram rising ste excitation and the focal waveforms for this excitation is resented in Figure 3. We can easily extend this result for the four 60 TEM feed arm case by multilying all the values by Analytical Focal Waveforms for Various Source Waveforms Driving a Prolate-Sheroidal IRA [8] We consider the time domain characteristics of some analytic source waveforms used for determining the waveform characteristic of a rolate-sheroidal IRA at the second focus. This is an analytical calculation of a rolate-sheroidal IRA that is based on Baum [2007, 1998], Farr [1993], and Altunc and Baum [2006b]. The analytical waveforms for the two-tem-feed-arm and 60 four-tem-feed-arm cases at the second focus are calculated. We analyze the analytical focal waveform behavior for two different source waveforms Double Exonential Excitation (DEE) [9] Let us use the commonly used waveform, which is the difference between two exonentials multilied by a unit ste function instead of a unit ste function as VðÞ¼V t 0 fðþ; t fðþ¼ t e bt e at ut ðþ; a ¼ t 1 d ; t d ¼ 100 s; 50 s; b ¼ td 1; t d ¼ 1ns; 2ns; ð6þ where t d is the risetime and t d is the decay time constant. The eak of the waveform is given by (2.14) in Baum [1976] as f max ¼ max ðfðþ t Þ ¼ z 1 t z ¼ b=a; 1 z 1 z 1 ¼ fðt max Þ; ð7þ where t max is the time when the maximum occurs and can be found by taking the derivative of (7) t max ¼ 1 a b ln a : ð8þ b We resent f (t)/f max value in Figure 4. 3of9

4 on Baum [2007] and Altunc and Baum [2006a]. We use maximum t mr (based on maximum rate of rise) as t d to comare our exerimental results with analytical results. For a ste like f(t), the t mr is t mr ¼ df dt f max : max ð11þ Figure 4. Double exonential excitation for f(t)/f max Analytical Focal Waveforms [10] From a ste excitation u(t) and DEE resonse of a rolate-sheroidal IRA at the second focal oint are comosed of three arts, the reulse, imulse and ostulse, as indicated in Figure 5. [11] One can see from Figures 5a and 5b that if we use a DEE instead of a ste excitation we have a decrease in the amlitude of the reulse, an increase in the amlitude of the imulse and the ostulse goes to zero. By modifying the excitation waveform we require less energy, but obtain a larger imulse amlitude. [12] The imulse art of the double exonential excitation is E d dv ðt t 2 Þ ¼ E h i d be b ð t t 2 Þ þae a ð t t 2Þ ut ð t 2 Þ f max dt f max ð9þ The exeriment uses three comonents: a rolatesheroidal reflector with feed arms, a samling-oscilloscoe, and a ulse generator. As seen from Figure 6, we use a Tektronix TDS 8000B Digital Samling-Oscilloscoe with a Tektronix 80E04 samling head to measure the waveform at the second focal oint. A Picosecond Pulse Labs ulser with a PSPL 4050 RPH fast ulser head generator is used for excitation. Figure 7 shows the 60 four-feed arm rolate-sheroidal IRA. The outut of the ste generator is a 45-s risetime, 10 V amlitude. We have also used a 10 db attenuator to decrease the voltage level for safety reasons. We use three tyes of and the eak value is E d (a b), where t 2 = 4.2 ns is the time when the imulse, arrives at the second focus. Finally, we obtain resonse waveforms from (9) in Figure 5a, E d ¼ E h i e b ð t 2 t 1 Þ e a ð t 2 t 1 Þ ð10þ f max where E d is the value of E at the time the imulse starts and t 1 = 2.5 ns is the time that reulse arrives at the second focus. 5. Exeriments [13] Exeriments were erformed using two-arm and 60 four-arm rolate-sheroidal IRAs and these results are comared with analytical results in Baum [2007]. This section resents a summary of the exerimental setu and the dimensions of these exeriments are based Figure 5. (a) Ste and (b) DEE resonse of a rolatesheroidal IRA at the second focal oint. 4of9

5 Figure 6. Exerimental setu for a two-feed arm rolate-sheroidal IRA. robes to measure the field: B-Dot Probe (EG&G MGL S7(R), equivalent area Aeq = m 2 and a risetime <150 s), slow D-Dot (Aeq = m 2, risetime <150 s) and fast D-Dot (Aeq = m 2, risetime <15 s) robes. [14] Figures 8 and 9 show that the results for the focal waveforms are close to one another but for the slow D- Dot sensor we do not have much oscillation in the ostulse since this robe has a slower frequency resonse comared with the other two. The measurements Figure 7. Exerimental setu for a 60 four-feed arm rolate-sheroidal IRA. 5of9

6 which may not be attributable to the different tyes of sensors that we are using. There will always be oscillations and aberrations in the signal observed in the fast D-dot robe. There are cable and connection non-uniformities, nonlinear effects in the samler, samling time errors, digitizing errors, etc. Most imortantly, the generator signal is not ure and has some aberrations following the ste voltage. [16] The slow sensors are more sensitive than the fast D-Dot sensor, but they are not fast enough to obtain the minimal t mr values. We observe larger t mr values, which result in a decrease in the amlitude of the imulse art of the focal waveform. If we use the fast D-Dot sensor we obtain higher amlitudes in the imulse art, but we obtain larger differences between the amlitudes of the imulse art of the analytical and exerimental focal waveforms. The average value of the analytical eak, exerimental results, oscillation amlitude, t mr and Figure 8. B-Dot Probe analytical, numerical and exerimental focal waveforms, E eq for (a) two-arms (t mr = 119 s), and (b) 60 four-feed arms (t mr = 127 s) rolate-sheroidal IRA. of the magnetic field are converted to an equivalent electric field as E eq ¼ cb ð12þ for convenient comarison with the measured electric field. Here B is the magnetic flux density. The equivalent electric field gives the exact result for the reulse because we have a TEM wave and E/H = h W for free sace. We calibrate our D-Dot data by comaring the reulse term. Although we do not have TEM waves for the imulse, we calculate h = E/H. For the two-arm case h is observed to be 384 W and for the four-arm case h is observed to be 408 W. This shows that we do not have a urely TEM wave for the imulse. The B-Dot data is believed to be accurate to a few ercent based on manufacturers calibration, and is also accurately calculable [Thomson and Luessen, 1986], at least below the uer bandwidth. [15] One can see from Figure 10 that when we use the fast D-Dot sensor we have an oscillation that is resent Figure 9. Slow D-Dot robe analytical, numerical and exerimental focal waveforms, for (a) two-arms (t mr = 119 s), and (b) 60 four-feed arms (t mr = 130 s) rolate-sheroidal IRA. 6of9

7 transmission coefficient of the reflector; however, there might be some ortions that do not reflect very well and this could cause some errors. 6. Numerical Simulation [19] We comare our analytical, numerical and exerimental focal waveforms for a two-arm rolate-sheroidal IRA in Figures 8 and 9. One can see by comaring the analytical, numerical and exerimental focal waveforms that the reulses agree very well. The analytical and numerical imulses amlitudes agree as well. However, the exerimental imulse amlitude is less than the others. It is also broader near the base. As discussed before, any misshae of the reflector may lead to this in the exeriment or exerimental inaccuracies also due to details of the excitation waveform. Figure 10. Fast D-Dot robe analytical and exerimental focal waveforms, for (a) two-arms (t mr = 26.5 s), and (b) 60 four-feed arms (t mr = 22 s) rolatesheroidal IRA. differences in exerimental results comared with the analytical results are summarized in Table 1. [17] There are several factors that can lead to differences in the analytical exressions and exeriments. When the focal fields are calculated in Baum [2007], the aerture integral did not consider the feed arms and feed-arms thicknesses. This can cause an error in the calculation of the imulse amlitude of the focal waveform. There are errors in the exeriment for which one needs to account. We are at the limit of our measurement instrumentation and we have less accuracy because of the limitation of the robes and ulse generator. [18] The geometric shae or alignment of the rolatesheroidal reflector may also cause some errors. Any misshae of the reflector will lead to a broader focus and smaller amlitude. The rolate-sheroidal reflector was manufactured from fiberglass and the inside of the reflector is ainted with coer conductive aint. We checked the reflection from the conductive aint on the reflector and calculated about 99% reflection using the 7. Conclusion [20] In this aer we have designed, constructed and tested a rolate-sheroidal IRA that was designed to assess this method s feasibility as art of a technique to kill skin cancer using ulsed electric fields. This work used analytical calculations, numerical simulations and exeriments. [21] The analytical behaviors of the focal waveforms of the two and four-feed arm rolate-sheroidal IRAs were calculated. The analytical waveform was illustrated and analyzed. These analytical calculations were for a two-arm rolate-sheroidal IRA. However, we have shown that these calculations can be easily extended to the 60 four TEM feed arm case by just multilying the analytical values by [22] Finally, the time domain characteristics of some analytic source waveforms used for determining the waveform characteristic of a rolate-sheroidal IRA at the second focus were discussed. With aroriate choice of a driving waveform we can maximize the imulse field at the second focus. Table 1. Average Value of the Analytical Peak, Exerimental Results, Oscillation Amlitude, t mr and Difference in Exerimental Results Comared to Analytical Results Average Value of the Analytical Peak Ex Results Oscillation tmr Difference (V/m) (V/m) (s) (%) B-Dot 2 Arm B-Dot 4 Arm D-Dot 2 Arm slow D-Dot 4 Arm slow D-Dot 2 Arm fast D-Dot 4 Arm fast of9

8 [23] We erformed several exeriments at the UNM Transient Antenna Laboratory in order to comare our analytical and numerical results. Exeriments with a twoarm and 60 four-arm rolate-sheroidal IRA were erformed. Exerimental, analytical and numerical results were comared. The small differences between these results were discussed and the differences were analyzed. Aendix A: Preulse Term E 2 After the Imulse [24] What haens to the reulse term after the imulse, i.e., after the truncation at the aerture boundary (Y = Y, or b for secial case)? This was not treated in Baum [2007]. Before the aerture truncation the reulse is given by E in (3). [25] Let E t = tangential E field (x comonent) on S a due to the reulse wave. Then we have [Baum, 2007, 1987] E 1 ¼ 1 E 2 ¼ 1 Z 2 S a S a z 0 z r2 2 E t ds ¼ 0 after wave asses z 0 z r2 2 E t ds ¼ ste wave left after the wave asses the aerture lane: ða1þ These are both integrals of the fields from the first focus on the aerture lane. After we see the edge of S a, neglecting diffraction terms from this edge and aroximating E t by the negative of the TEM reulse wave out to this edge (for a ositive arameter as in Baum [2007]) we have, for ste-function excitation, a timeindeendent reulse field on S a, E 1 ¼ 0; the derivative being zero after the aerture edge is seen E 2 ¼ 1 Z z0 z 2 r2 3 E t ds ¼ constant; i:e: a ste term: ða2þ Next we require the static E 2. As before, since we are confining ourselves to the z axis we can use a uniform field on the rojection lane to give E 2 in the above integral. From (2.11) of Baum [2007] at r 1 = z 0 (aerture lane center) E a0 ffi V 0 tan q c : ða3þ z 0 f g 2 This can be extended over S a since, as we have seen before [Baum, 2007], for the z axis only the uniform field terms (on the rojection lane) need be considered (by symmetry). [26] In the end we obtain E 2 ¼ V 0 1 b h 1 þ z i : ða4þ 2f g z 0 a þ z 0 b Let us find the ratio of E 2 /E from (A4) and (3) E 2 b 2 h ¼ 1 þ z i a z 1=2 : ða5þ E a þ z 0 b a þ z For our case (1) E 2 E ¼ 0:16 < 1; ða6þ as exected, we have almost an 85% decrease in the reulse after the imulse. References Altunc, S., and C. E. Baum (2006a), Extension of the analytic results for the focal waveform of a two-arm rolate-sheroidal imulse-radiating antenna (IRA), Sens. and Simul. Note 518, De. of Electr. and Comut. Eng., Univ. of N. M., Albuquerque, Nov. Altunc, S., and C. E. Baum (2006b), Comarison of analytical and numerical results for a rolate-sheroidal imulse-radiating antenna (IRA), Sens. and Simul. Note 519, De. of Electr. and Comut. Eng., Univ. of N. M., Albuquerque, Nov. Baretela, M. J., and J. S. Tyo (2003), Imrovement of romt radiated resonse from imulse radiating antennas by aerture trimming, IEEE Trans. Antenn. Proag., 51, Baum, C. E. (1976), Some considerations concerning analytical EMP criteria waveforms, Theoretical Note 285, De. of Electr. and Comut. Eng., Univ. of N. M., Albuquerque, Oct. Baum, C. E. (1987), Focused aerture antennas, Sens. and Simul. Note 306, De. of Electr. and Comut. Eng., Univ. of N. M., Albuquerque, May. Baum, C. E. (1998), Radiation of imulse-like transient fields, Sens. and Simul. Note 321, De. of Electr. and Comut. Eng., Univ. of N. M., Albuquerque, Nov. Baum, C. E. (2007), Focal waveform of a rolate-sheroidal imulse-radiating antenna (IRA), Radio Sci., 42, RS6S27, doi: /2006rs Baum, C. E., E. G. Farr, and D. Giri (1999), Review of imulseradiating antennas, in Review of Radio Science , edited by W. R. Stone, , Oxford Univ. Press, New York. Baum, C. E., et al. (2004), JOLT: A highly directive, very intensive, imulse-like radiator, in Proceedings of IEEE Secial Issue on Pulse Power: Technology and Alications, vol. 92, , De. of Electr. and Comut. Eng., Univ. of N. M., Albuquerque, July. 8of9

9 Farr, E. G. (1993), Otimizing the feed imedance of imulse radiating antennas, art I. reflector IRAs, edited by C. E. Baum, Sens. and Simul. Note 354, Phillis Lab., Albuquerque, N. M. Kim, K., and W. R. Scott (2003), Analysis of imulse-radiating antennas with ellisoidal reflectors, Sens. and Simul. Note 481, De. of Electr. and Comut. Eng., Univ. of N. M., Albuquerque. Schoenbach, K. H., R. Nuccitelli, and S. J. Beebe (2006), Za, IEEE Sectr., 43(8), Thomson, J. E., and L. H. Luessen (1986), Fast Electrical and Otical Measurements, vol. 1, , Martinus Nijhoff, Leiden, Netherlands. Tyo, J. S., and C. J. Buchenauer (2002), Exerimental verification of the effect of aerture shae on romt IRA resonse, IEEE Trans. Antenn. Proag., 50, S. Altunc, C. E. Baum, C. J. Buchenauer, C. G. Christodoulou, and E. Schamiloglu, Deartment of Electrical and Comuter Engineering, University of New Mexico, Albuquerque, NM 87131, USA. 9of9