Ph.D Dissertation proposal

A new compact, portable 2-LTD-brick x-pinch driver at

the Idaho Accelerator Center: design, fabrication, testing

and x-ray performance

Roman V. Shapovalov

Physics Department

Idaho State University

Adviser: George Imel, Ph.D

Co-adviser: Rick Spielman, Ph.D

Committee: Mahbubul Khandaker, Ph.D

Committee: Khalid Chouffani, Ph.D

GFR: DeWayne Derryberry. Ph.D

October, 2014

II

Contents

Abstract ........................................................................................................................................................ III

1. Introduction .......................................................................................................................................... 1

2. Design and fabrication .......................................................................................................................... 3

2.1. Electrical design approach ............................................................................................................ 3

2.2. 2 LTD driver: electrical circuit and simulation .............................................................................. 3

2.3. 2 LTD driver: mechanical design and fabrication .......................................................................... 5

3. Driver testing and characterization ...................................................................................................... 7

3.1. Pulsed-current diagnostic ............................................................................................................. 7

3.2. Short circuit test data .................................................................................................................... 8

3.3. Revised driver model and projected x-ray performance .............................................................. 9

4. Summary and future works ................................................................................................................ 11

Bibliography ................................................................................................................................................ 12

III

ABSTRACT

There is a great interest in an x-pinch x-ray radiation source for use in a variety of applications

where a bright, sub-nanosecond, and μm radiation source pulse is needed. Some examples include

point-projection radiography in plasmas, imaging of soft biological objects, characterization of

inertial-confinement-fusion capsule shells, and more. However, because almost all well-known,

“standard” x-pinch radiation machines are based on a conventional Marx generator, they are large,

expensive to build, operate, and are therefore not easily available for all laboratories where an x-

pinch radiation source is required. Some small x-pinch generators exist, but they still lack

portability.

Literature suggests that current rise rate, dI/dt, of 1 kA/ns or more is required for a "good" x-

pinch radiation performance. For reasonable current rise times, this translates to a current

requirement of 150 kA or more. We propose to construct a compact and portable x-pinch driver

with x-ray radiation performance, comparable to standard x-pinch drivers. Such a new x-pinch

driver was recently designed, fabricated and tested at the Idaho Accelerator Center. The generator

is based on two slow LTD bricks combined into one solid unit, and can be described by a simple

RLC circuit with four fast 140-nF, 100-kV capacitors that store up to 2.8 kJ. The test data reveals

that when charged to 80 kV, the driver supplies 185-kA peak-current into a short Ni-wire load with

220-ns, 10-90%, rise time. The total internal inductance of our driver was measured to be about

60 nH. The revised driver model shows that when fully charged to 100 kV, the driver will supply

180-kA peak-current with 150-ns rise-time into the x-pinch load. The corresponding current rise

rate is about 1.2 kA/ns.

To prove the driver x-pinch efficiency and to estimate the x-ray radiation performance, we

could, for example, image an exploding wires, placed in a separate HV pulser, with our x-pinch x-

ray radiation source. The study of exploding wires helps to understand the behavior of a warm

dense matter, and our x-pinch driver can be part of the diagnostics needed for this study which is

currently under progress at the IAC. Our driver contains no oil inside, is very compact and portable,

and can be easily relocated to practically anywhere, which makes it an ideal backlighting

diagnostic tool in many areas of plasma physics, biology, and industry where a bright, fast, and

small x-pinch radiation source is required.

Keywords: x-pinch, pulse power generator, LTD driver, x-ray plasma radiation source, x-pinch

backlighting.

1

1. INTRODUCTION

The x-pinch, x-ray radiation source (in which the crossing and touching of two or more thin

wires forms an “x”, hence, x pinch) was first introduced by Russian physicists at Lebedev Physical

Institute [1], and has since generated a great interest in many areas of plasma physics, biology, and

industry. When a high, fast rising current is passing through x-pinch wires, a very fast, small and

bright x-ray radiation source is produced. The width can vary from a few ps to tens of ns, the

source size could be as small as a few μm, radiation power is on the order of a few hundred mJ,

and the energy spectra ranges from soft to hard x-rays. All these radiation parameters are especially

useful, when a high temporal and spatial resolution is desired to study many different, fast

evolving, low opacity objects which makes the x-pinch, x-ray radiation source an unique diagnostic

tool in many areas of researches. Some known x-pinch applications include, but not are limited to:

point-projection radiography of exploding wires [2-8], backlighting of other x-pinch [9-13] or even

z-pinch [14-16] systems, phase-contrast imaging of soft biological objects [6, 9, 17, 18], studying

low density CH foams on an axis of wire array z-pinches [19], characterization of inertial-

confinement-fusion capsule shells [20], or and even microlithography [21].

For a long time, a conventional pulsed-power device for driving an x-pinch load was a high-

voltage Marx generator coupled with one or more transmission lines to compress an initially long

(few µs) pulse from the generator’s output into a short (a few hundred ns) pulse at the load.

XP pulser [22, 23], for example, operating at Cornell University, consists of a 10-stage Marx

generator, 4 coaxial intermediate storage capacitors, 3 coaxial pulse forming lines, one self-

breaking gas switch, and 8 self-breaking water switches. It was designed and built about 20 years

ago and can delivery about 450 kA with a 40-ns, 10-90%, rise time to a low inductance load. The

Llampudken [24, 25] high-current pulser at Pontifical Catholic University in Chile consists of two

Marx capacitor banks with a water transmission line coupled with each Marx generator, and it can

supply about 400-kA peak current with a 260-ns rise time. Recently built at Tsinghua University

in Beijing, China, PPG-1 [26, 27] is composed of a 1.2 MV Marx generator, pulse forming line,

transmission line, switch, and a load section, and it can supply a 400-kA peak-current with a 100-

ns pulse-width. Some other known pulsed-power installations used in x-pinch researches are

LION [28], a 470-kA 80-ns pulser at Cornell; COBRA [29], a 1-MA, 100-ns generator at Cornel;

Gamble II, a 1-MA, 100-ns pulser at the Naval Research Laboratory, in Washington DC;

ZEBRA [30, 31], a 1.2-MA, 90-ns pulser at University of Nevada; MAGPIE [32, 33], a 1.8-MA

150-ns TeraWatt facility at Imperial College; S-300 [34], a 2.3-MA 150-ns high-current generator

at Lebedev Physical Institute, in Moscow, Russia; and more. Examples of smaller x-pinch drivers,

which can deliver a current up to 200 kA are a 80-kA 50-ns X-Pinch Pulser [35, 36] at the

University of California, San Diego; 100-kA 60-ns table-top x-pinch [6] at Tsinghua University,

China; GEPOPU [37], a 180-kA, 120-ns low inductance pulser at Pontifical Catholic University,

Chile; and Light-II [38], a 200-kA pulsed-power generator at China Institute of Atomic Energy

(CIAF), Beijing, China.

All such pulsed-power systems are able to deliver a large, fast rising current to a low inductance

x-pinch load and have generated for decades a huge amount of x-pinch research around the world.

But, in summary, all these x-pinch installations, are based on conventional Marx generators, water

forming lines, and gas switches, all of which have many drawbacks. Some of them [22-34] are

huge and bulky, and therefore are expensive to build and operate. Others [36-38] are more

compact, but they are still require a conventional Marx generator filled with oil, water transmission

lines, and gas system, which is often inconvenient. Large drawbacks of all such systems are that

they still lack portability and are usually limited to one location to conduct experiments. Indeed,

our initial design of x-pinch plasma-radiation-source generator [39] was based on an idea to non-

destructively convert the Idaho State Induction System (ISIS) induction cell driver (ICD) to a low-

2

impedance pulsed-power driver. Such a system would be composed of Marx generator, 5 pulse

forming lines coupled to an impedance converter, and would supply about 200-kA peak-current

with a 60-ns, 10-90%, rise time [39] into an x-pinch load. But, if constructed, it would be a large,

fixed facility, located at the ISIS IAC site, which would be difficult to relocate to another place if

needed.

Recent progress in the development of low-inductance, high-current capacitors [40-42] and

switches [43-46] opens up big opportunities in the design of new pulsed-power generators, which

can directly supply a high-current pulse into a low-inductance x-pinch load. For example,

PIAF [47-48], built at Cole Polytechnique, France, is a LC generator, based on total of 6, low

inductance 180-nF, 50-kV capacitors connected in parallel, which can deliver a 250-kA, 180-ns

high-current pulse to an x-pinch load without use of any water transmission lines. GenASIS [49],

University of California, San Diego, is a 200-kA 150-ns rise time x-pinch driver composed of 12

General Atomics, 20-nF, 100-kV capacitors directly arranged around a load section. A compact

pulse generator [50], Tomsk, Russia, is based on 4 fast, high-current capacitors and able to supply

about 300-kA peak-current with 200-ns rise-time. SPAS [51] current generator at Lebedev

Institute, Russia, includes four parallel-connected capacitor-switch assemblies placed in a common

tank and delivers about 250-kA peak current with 200-ns rise-time into an x-pinch load.

MAIZE [52] at University of Michigan, can deliver a huge, up to 1-MA peak-current into x-pinch,

and even z-pinch loads.

Such new pulsed-power generators [47-52] offer many advantages, compared to conventional

Marx-based systems. For example, lower capacitor voltage allows one the building of a pulsed-

power generator without an isolation oil; being based on low inductance capacitors and switches,

such drivers can directly drive a low-inductance x-pinch load; no needs for transmission lines

allows the elimination of the water conditioning system. Some of these pulsed-power drivers [49,

52] are based on modular, linear transformer driver (LTD) architecture. The basic building block

of such systems, called LTD "brick", is usually composed of two capacitors connected in parallel

followed by a triggered switch. The brick can be charged up to 100 kV and deliver up to 100-kA

peak-current, and it serves as a building block to construct more complicated, pulsed-power

systems [53-56]. Most importantly, all these considerations (new low-inductance capacitors and

switches, LTD "brick" technology) allows one to design and build compact, non-expansive x-pinch

drivers which can replace old, conventional, bulky, and expensive pulsed-power systems [22-38].

Our goal is to design and build a compact, portable x-pinch radiation source generator with a

"good" x-ray radiation performance, comparable to standard x-pinch drivers. While many

experiments have been devoted to studying how x-pinch radiation parameters correlate with wire

materials, mass, and geometries [2-8, 57-62], they are usually done using one pulsed-power

generator, available in each particular case. The literature [2-38, 47-52, 57-63] suggests that a

minimum current rise rate, dI/dt, of 1 kA/ns is required to achieve a "good" x-pinch x-ray radiation

performance. For reasonable current rise times, this translates to a current requirement of 150 kA

or more. Our initial design uses the recent development of low-inductance, high-current capacitors

and switches, as well as the concept of simple, “matched” RLC circuit [64-65] and was described

elsewhere [66]. Our final design is based on 2 slow LTD bricks (total of 4 capacitors) combined

into a one, solid unit and was reported recently [67]. The new idea behind our x-pinch driver design

is that it can be truly compact, portable, and available for all activities where an x-pinch radiation

source is needed. As far as we know, no such portable x-pinch drivers currently exist.

3

2. DESIGN AND FABRICATION

2.1. Electrical design approach

In our design approach, we are following the description introduced by M. G. Mazarakis &

R. B. Spielman [64-65]. For a small generator without long transmission lines, the whole generator

with the load can be approximated by a simple RLC circuit. A pulse generator with a “matched”

load 𝑅 = √𝐿/𝐶 is, in general, able to produce higher pulse currents with faster rise times compared

to the “critically matched” 𝑅 = 2√𝐿/𝐶 case, and is more suitable for the design of a radiographic

x-pinch machine [65]. In the “matched” case the peak current and time-to-peak, are given by the

following expressions [65]:

/RV0.546i 0peak , (1)

LC1.21tpeak , (2)

where V0 is the initial voltage of capacitor C.

To prove this approach, we initially designed [66] a compact plasma-radiation-source

generator, based on only four, fast high-current capacitors discharged simultaneously in parallel

into a “matched” x-pinch load. The simulation shows [66] that the driver supply about 180-kA

peak-current with a 150-ns time-to-peak into an x-pinch load.

2.2. 2 LTD driver: electrical circuit and simulation

Our final design is based on 2, slow LTD bricks (total of 4 capacitors) that was reported

recently [67]. The electrical circuit is shown in Fig. 1 and described below.

FIGURE 1. 2-LTD-brick x-pinch driver electrical diagram.

Each brick is comprised of two GA 35465 capacitors and one multi-gap, air insulated switch.

The rated voltage of each capacitor is 100 kV, the rated peak current is 50 kA, capacitance is

140 nF, and inductance is about 20 nH. The inductance of each switch is about 15 nH. The “bare”

bricks inductance, Lbrick, is equal to 25 nH and the extra inductance of all elements, Lextra, which

includes extra inductance of bricks placed inside the finite volume, anode-cathode inductance and

inductance of all other connections, is estimated to be about 12 nH. The total internal inductance

of our x-pinch generator is:

4

nH5.24nH)122/25(2/ extrabrickdriver LLL . (3)

The inductance of the x-pinch load is estimated to be about 10 nH with a resistance 0.24 Ω.

These numbers corresponds to an x-pinch load comprised of two 11-mm-long, 40-µm-diameter

Mo wires in the initial “cold” state. The real values will be different depending on the electrical

parameters of the real “hot” wire state. The total inductance of the whole driver, including the x-

pinch load, is:

nH5.34nH)105.24( pinchxdriver LLL . (4)

LTSpice [68] simulations of our driver are presented in Fig 2. The driver can supply 220-kA

peak-current with about 170-ns time-to-peak value when it is fully charged to 100 kV. The peak

power at the x-pinch load is about 11.6 GW, and the energy transferred to the load by the time to

peak is about 1.1 kJ. That is about 39% percent of the total 2.8-kJ energy, which can be initially

stored inside capacitors. The proposed driver is naturally very efficient and almost half of the initial

energy is transferred to the load by the time to first peak.

FIGURE 2. LTSpice simulation of 2-LTD-brick driver. Red line is the output load current, blue is the output

power, black (dotted) is energy transferred to the load.

The parameters simulated above of the x-pinch generator, such as a peak current and a rise

time, can be easily predicted and verified by the simple RLC model described above. The

“matched” x-pinch load value of our generators equals 0.25 Ω and, according to formulas (1, 3),

the peak current and rise time can be calculated as:

kA218kV/0.251000.546ipeak , (5)

ns168nF 560nH 34.51.21tpeak , (6)

which are in a good agreement with the values simulated above.

5

2.3. 2 LTD driver: mechanical design and fabrication

The mechanical design of our x-pinch x-ray generator is based on the desire to make the driver

compact and portable and to minimize the total driver inductance. We used 2, slow NRL LTD

bricks [69] combined into one, solid unit. The x-pinch driver assembly is pictured in Fig. 4. Bricks

are placed inside the steel housing with ground and output plates on opposite sides. The vacuum

chamber is placed at the top of the output plate and is designed to withhold a low vacuum needed

for x-pinch x-ray generation. It is composed of a 6" in diameter, cylindrical body and two 2-3/4"

output ports.

FIGURE 3. 2-LTD-brick x-pinch x-ray generator, general view. Left - drawing, right – image.

The output section of x-pinch x-ray generator is presented in Fig. 4. The high voltage plate

combines 2 bricks and feeds the output current into the load section. A ¾" isolating acrylic plate

is placed between the high voltage and output plates. A 2" long, 2" diameter cathode section is

attached to the high voltage plate. The anode section is 1-3/4" long, has the 2-1/2" inner diameter

and has two output x-ray windows aligned with vacuum chamber output ports.

6

FIGURE 3. The output cross-section view of 2 LTD bricks x-pinch x-ray generator.

To minimize the driver inductance, the anode-cathode gap was reduced to 6.3 mm. With such

a small A-K gap, the power feed must operate in the self magnetically insulated mode. The 𝒗 × 𝑩

Lorentz force induced by a current pulse will turn back electrons emitted from the cathode and

stop the voltage breakdown in the inter-electrode space. The minimum operating current,

according to [47], can be estimated to be:

ca RR

VI

/ln

)kV(64.0min . (7)

where Ra and Rc are anode/cathode diameters. With the present geometry, the minimum operating

current becomes:

)kV(87.2min VI . (8)

At a maximum anode-cathode voltage of 55 kV, for the magnetic self-insulating principle to

work, the minimum operating current becomes 21 kA. This is well below the predicted (5) 220-

kA value.

All x-pinch driver parts were carefully designed using SolidWorks 2013 [70], 3D solid

modeling engineering software. A total of 41 drawings needed for x-pinch driver fabrication were

generated, and are stored at IAC backup server and can be requested, if needed.

7

3. DRIVER TESTING AND CHARACTERIZATION

3.1. Pulsed-current diagnostic

An electrostatically shielded Rogowski coil [71-72] with a very good signal-to-noise ratio was

designed and placed at x-pinch driver output section to measure the total current delivered into an

x-pinch load. Our Rogowski coil has a total of 29 turns with 1-inch winding spacing. To calibrate

the Rogowski coil, the set-up (shown in Fig. 5) was used. A total of 5 fast, 30 nF, HV capacitors

were initially charged to 5 kV to produce high-current oscillations. A 0.1003-Ω calibration current

viewing resistor (CVR) was placed at the end of the metal strip line. This set-up allowed us to

reach a 360-ns time-to-first-peak value which is close to the x-pinch driver parameter.

FIGURE 4. Rogowski coil calibration set-up.

The calibration data are shown in Fig. 6. The output Rogowskii coil signal is proportional to

dI/dt and should be integrated to get a current waveshape. The special calibration method was

developed to reasonably fit the Rogowski integral to CVR current. The Rogowski coil calibration

factor is found to be 2.51.

FIGURE 5. Rogowski coil calibration data; blue line – CVR current, black line – Rogowski output signal in V; red

line – Rogowski integral normalized to match CVR current.

8

3.2. Short circuit test data

Several configurations of a 2-LTD-brick x-pinch driver were tested before a good “working”

configuration was found. To show the general progress as the driver configuration was improved

from test to test, test data are briefly summarized in Table 1. Initial tests (test 1-3) were done with

1-Ω resistor immerged in dielectric oil. Tests 4 and 5 were performed with a salted water load

filled the anode-cathode gap and the lower part of the cathode feed. To reduce the total driver

inductance, starting from test 5, the Cu sheet was placed between two bricks inside the brick

housing. TABLE 1. 2-LTD-brick x-pinch driver tests data.

Date, 2014 Load Short #

/kV Ipeak

(kA) Tpeak (ns)

dI/dtmax (kA/ns)

Comments and common problems

Test 1 May 12-13

1 Ω HVR

3/76 47 300 0.40 Common charging line, pre-fire, HV plate spark, only 1

brick is fired;

Test 2 Jun 11 1/80 72 420 0.35 Separate charging line, non-pre-fire, HVR spark, 2 bricks are fired differently in time;

Test 3 July 17 2/78 40 290 0.30 Same as test 3, but no HVR spark, 2 bricks separation time

~ 1.1 us; resister is expanded;

Test 4 July 24 Salted water

R1 R2

R3

R4 R5

R6

6/80 11/80

18/80

22/80 29/80

39/80

153 150

144

124 115

100

382 386

382

377 365

360

0.71 0.66

0.60

0.58 0.56

0.53

Sparking at the end of trigger line eliminated, all bricks are

fired simultaneously;

Test 5 Aug 1 R 4/80 170 335 0.91 Cu sheet is placed between two bricks to reduce the system inductance, 2 PT-55;

Test 6 Aug 14 Wire load in

oil 6/80 185 370 0.86 Configuration is the same as in test 5;

The final test 6, for short event 3, is discussed in more details below. The bricks were initially

charged to 80 kV and the load was a 1.48-cm-long, 2.9-mm-diameter Ni-wire. The experimental

data are presented in Fig. 7. The Rogowski peak current is about 185 kA with 220-ns, 10-90%,

rise time. The corresponding current rise rate is 0.84 kA/ns.

FIGURE 6. 2-LTD-brick driver test data with wire load, 08/14/2014, short 3, 80 kV; black line – Rogowski output

current, kA/ns, red line – Rogowski current integral, kA.

To better understand the driver parameters, LTSpice simulations were compared with

experimental data and results are presented in Fig. 8. The total driver inductance and resistance

9

values were varied until good agreement with measured oscillation time and decay constant was

achieved. The inductance and resistance values were found to be 69 nH and 0.042 Ω,

correspondingly. However, simulations cannot reproduce the initial capacitors charge 80 kV. Most

likely, there were some losses inside the driver which effectively reduced the initial voltage down

to about 71 kV. After 5 µs, the experimental current starts to deviate from simulated one. This can

be explained by changes in the switch resistance, which starts to increase at the end of the current

pulse.

FIGURE 7. Comparison of experimental current with LTSpice simulation; red line – Rogowski current,

08/14/2014, short 3, 80 kV; blue (dotted) lines – LTSpice simulation.

The total internal inductance of our 2-LTD-brick x-pinch driver can be estimated as follow.

The inductance value found above, 69 nH, is the total driver inductance, which includes the wire

load value. The wire load inductance can be estimated as:

nH12.9ln21

0 r

rhLload . (9)

where, h is the wire length, 1.48 cm, r1 is the wire diameter, 1.45 mm, and r0 is the inner anode

diameter, 31.75 mm. So, the total internal driver inductance should be equal to:

nH60nH)12.969( loadmeasureddriver LLL . (10)

3.3. Revised driver model and projected x-ray performance

The 2-LTD-brick driver model was revised based on the short-circuit test data. The electrical

circuit diagram, presented in Fig 1, was modified to match the total internal driver inductance to

the measured 60-nH value. The total driver inductance, including x-pinch load, was 70 nH. The

simulations are presented in Fig. 9 and briefly discussed below.

10

FIGURE 8. LTSpice simulation of 2 LTD bricks driver. Red line is the output load current, blue is the output

power, black (dotted) is energy transferred to the load.

As can be seen, the driver, when it is fully charged to 100 kV, can supply 180-kA peak-current

with about a 150-ns, 10-90%, rise time. The corresponding current rise rate, dI/dt, equals 1.2 kA/ns,

which is close to the measured value of 0.84 kA/ns when it scaled to 100 kV. The peak power at

the x-pinch load is about 7.7-GW, and the energy transferred to the load by the time to peak is

about 1.2 kJ. That is 43% percent of the total 2.8 kJ of energy initially stored inside capacitors.

The projected x-pinch performance of our 2 LTD x-pinch driver is presented in the Fig. 9. The

data are taken from PIAF generator [47] which can supply about 250-kA peak current to a 6-nH

inductive load with a 180-ns current rise time. For the load composed of two 25-μm Mo wires, the

projected x-ray performance is at least 250-500 mJ in a pulse 1.2-2.0-ns FWHM for photon energy

above 700 eV [47].

FIGURE 9. Projected x-pinch performance from PIAF pulsed power generator. The load is two 25-µm Mo wires

and x-ray data is with a 3-μm Mylar filter.

11

4. SUMMARY AND FUTURE WORKS

The objective of this proposal is to develop a new, compact and truly portable x-pinch radiation

source generator with a "good" x-ray radiation performance; the radiation source should be fast,

small, and bright; and should be comparable to other standard x-pinch drivers. Below is a short

summary of what has been done and what is expected to make this research project a success:

Literature suggests that there is a need for compact and portable x-pinch radiation sources

for use in a variety of applications in physics, biology and industry. The current rise rate,

dI/dt, of 1 kA/ns or more is required for a "good" x-pinch radiation performance.

A new compact and portable x-pinch driver was recently designed and constructed at IAC.

Our final design is based on 2 "slow" LTD bricks combined into one, solid unit. The driver

inductance was minimized and the output load current was maximized. The size of our

driver is only 28x13x14 inches and it weighs about 200 pounds.

The test data reveals that the driver can supply 185-kA peak-current into a short wire load.

The rise time, 10-90%, is about 220-ns and the corresponding current rise rate is 0.84

kA/ns. The measured total internal inductance of our driver is about 60 nH.

The simulation, based on the revised driver model, shows that the driver can deliver about

180-kA peak current into an x-pinch load with a 150-ns, 10-90%, rise time. The

corresponding current rise rate is 1.2 kA/ns.

X-ray radiation parameters of constructed 2-LTD-brick x-pinch driver will be measured

and characterized for different wire materials and geometries. The data will be compared

with other well-known x-pinch drivers with a similar current-rise-rate.

The performance of constructed x-pinch driver as an x-ray backlighting tool will be

evaluated and reported. The study of an exploding wire is among all possible applications

of our constructed 2-LTD-driver. This study is currently under progress at the IAC, and

will help to better understand the EOS of a warm dense matter. We will image this plasma

with our x-pinch and will characterize the spatial and temporal resolution of our radiation

source.

The low cost of operation, compactness, and portability of the constructed 2 LTD x-pinch

driver will make it available for many experiments where a bright, fast x-ray source is

needed. As far as we know, no such portable x-pinch drivers currently exist.

12

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