Patent ID: 12245351

DETAILED DESCRIPTION

Various embodiments of plasma confinement systems and methods for their use are disclosed herein. The disclosed embodiments, when compared to existing systems and methods, may facilitate increased plasma stability, more robust sheared plasma flow, smaller Z-pinch plasma radii, higher magnetic fields, and/or higher plasma temperature. Some of the disclosed embodiments exhibit independent control of plasma acceleration and plasma compression as well.

FIG.1is a schematic cross-sectional diagram of a plasma confinement system100. The plasma confinement system100includes an inner electrode102and an outer electrode104that substantially surrounds the inner electrode102. The plasma confinement system100also includes one or more first valves106configured to direct gas from within the inner electrode102to an acceleration region110between the inner electrode102and the outer electrode104and two or more second valves112configured to direct gas from outside the outer electrode104to the acceleration region110. The plasma confinement system100also includes a power supply114configured to apply a voltage between the inner electrode102and the outer electrode104.

The inner electrode102generally takes the form of an electrically conducting (e.g., stainless steel) shell having a substantially cylindrical body116. The inner electrode102includes a first end118(e.g. a rounded end) and an opposing second end120(e.g., a substantially circular end). More specifically, the first end118may have a conical shape with a rounded tip. The inner electrode102may include one or more conduits or channels (not shown) for routing gas from the one or more first valves106to the acceleration region110.

The outer electrode104also generally takes the form of an electrically conducting (e.g., stainless steel) shell having a substantially cylindrical body128. The outer electrode104includes a first end122(e.g., a substantially disc-shaped end) and an opposing second end124(e.g., a substantially circular end). As shown inFIG.1, the first end118of the inner electrode102is between the first end122of the outer electrode104and the second end124of the outer electrode104. The outer electrode104surrounds much of the inner electrode102. The inner electrode102and the outer electrode104may be concentric and have radial symmetry with respect to the same axis. The outer electrode104may include one or more conduits or channels (not shown) for routing gas from the two or more second valves112to the acceleration region110.

The one or more first valves106may take the form of “puff valves,” but may include any type of valve configured to direct gas (e.g., hydrogen or deuterium) from within the inner electrode102to an acceleration region110between the inner electrode102and the outer electrode104. As shown inFIG.1, the one or more first valves106are positioned axially between the first end118of the inner electrode102and the second end120of the inner electrode102. Alternatively, the one or more first valves might be located at the first end118or the second end120of the inner electrode102. InFIG.1, the one or more first valves106are positioned within the inner electrode102, but other examples are possible. The one or more first valves106can be operated by providing the one or more first valves106with a control voltage, as described below.

The acceleration region110has a substantially annular cross section defined by the shapes of the inner electrode102and the outer electrode104.

The two or more second valves112may take the form of “puff valves,” but may include any type of valve configured to direct gas (e.g., hydrogen or deuterium) from outside the outer electrode104to the acceleration region110. As shown inFIG.1, the two or more second valves112are positioned axially between the first end122of the outer electrode104and the second end124of the outer electrode104. Alternatively, the two or more second valves may be located at the second end124or at the first end122. The two or more second valves112will generally be arranged around the outer electrode104. As shown inFIG.1, the one or more first valves106are axially aligned with the two or more second valves112, but other examples are possible. The two or more first valves112can be operated by providing the two or more second valves112with a control voltage, as described below.

The power supply114will generally take the form of a capacitor bank capable of storing up to 500 kJ or up to 3-4 MJ, for example. A positive terminal of the power supply114can be coupled to the inner electrode102or alternatively to the outer electrode104.

The plasma confinement system100includes an assembly region126within the outer electrode104between the first end118of the inner electrode102and the first end122of the outer electrode104. The plasma confinement system100is configured to sustain a Z-pinch plasma within the assembly region126as described below.

The plasma confinement system100also includes a gas source130(e.g., a pressurized gas tank) and one or more first regulators132configured to control gas flow from the gas source130through the respective one or more first valves106. Connections (e.g., piping) between the one or more first regulators132and the one or more first valves106are omitted inFIG.1for clarity.

The plasma confinement system100also includes two or more second regulators134configured to control gas flow from the gas source130through the respective two or more second valves112. Connections (e.g., piping) between the one or more second regulators134and the two or more second valves112are omitted inFIG.1for clarity.

The plasma confinement system100also includes an insulator136between the second end124of the outer electrode104and the inner electrode102to maintain electrical isolation between the inner electrode102and the outer electrode104. The insulator136(e.g., a ceramic material) generally has an annular cross section.

The plasma confinement system also includes a vacuum chamber138(e.g., a stainless steel vessel) that at least partially surrounds the inner electrode102and the outer electrode104, as shown inFIG.1.

FIG.2is a schematic cross-sectional diagram of a plasma confinement system200. The plasma confinement system200includes an inner electrode202, an intermediate electrode203that substantially surrounds the inner electrode202, and an outer electrode204that substantially surrounds the intermediate electrode203. The plasma confinement system200also includes one or more first valves206configured to direct gas from within the inner electrode202to an acceleration region210between the inner electrode202and the intermediate electrode203. The plasma confinement system200also includes two or more second valves212configured to direct gas from outside the intermediate electrode203to the acceleration region210. The plasma confinement system200also includes a first power supply214configured to apply a voltage between the inner electrode202and the intermediate electrode203and a second power supply215configured to apply a voltage between the inner electrode202and the outer electrode204.

The inner electrode202generally takes the form of an electrically conducting (e.g., stainless steel) shell having a substantially cylindrical body216. The inner electrode202includes a first end218(e.g. a rounded end) and an opposing second end220(e.g., a substantially circular end). More specifically, the first end218may have a conical shape with a rounded tip. The inner electrode202is generally similar to the inner electrode102discussed above. The inner electrode202may include one or more conduits or channels (not shown) for routing gas from the one or more first valves206to the acceleration region210.

The outer electrode204also generally takes the form of an electrically conducting (e.g., stainless steel) shell having a substantially cylindrical body228. The first end222of the outer electrode204is substantially disc-shaped and the second end224of the outer electrode is substantially circular. The outer electrode204surrounds much of the inner electrode202and much of the intermediate electrode203. The inner electrode202, the intermediate electrode203, and the outer electrode204may be concentric and have radial symmetry with respect to the same axis.

The intermediate electrode203generally takes the form of an electrically conducting (e.g., stainless steel) having a substantially cylindrical body229. The intermediate electrode203includes a first end219that is substantially circular and a second opposing end221that is substantially circular. The intermediate electrode203may include one or more conduits or channels (not shown) for routing gas from the two or more second valves212to the acceleration region210.

The first end218of the inner electrode202is between the first end222of the outer electrode204and the second end224of the outer electrode204. The first end219of the intermediate electrode203is between the first end222of the outer electrode204and the second end224of the outer electrode204.

The one or more first valves206may take the form of “puff valves,” but may include any type of valve configured to direct gas (e.g., hydrogen or deuterium) from within the inner electrode202to an acceleration region210between the inner electrode202and the intermediate electrode203. As shown inFIG.2, the one or more first valves206are positioned axially between the first end218of the inner electrode202and the second end220of the inner electrode202. Alternatively, the one or more first valves might be located at the first end218or the second end220of the inner electrode202. InFIG.2, the one or more first valves206are positioned within the inner electrode202, but other examples are possible. The one or more first valves206can be operated by providing the one or more first valves206with a control voltage, as described below.

The acceleration region210has a substantially annular cross section defined by the shapes of the inner electrode202and the intermediate electrode203.

The two or more second valves212may take the form of “puff valves,” but may include any type of valve configured to direct gas (e.g., hydrogen or deuterium) from outside the intermediate electrode203to the acceleration region210. As shown inFIG.2, the two or more second valves212are positioned at the second end221of the intermediate electrode203, but other examples are possible. The two or more second valves212are arranged outside of the outer electrode204and outside of the intermediate electrode203, for example. In other examples, the two or more second valves could be located inside the outer electrode and outside the intermediate electrode. The two or more second valves212are configured to direct gas between the first insulator236and the second insulator237. The two or more first valves212can be operated by providing the two or more second valves212with a control voltage, as described below.

The first power supply214and the second power supply215will generally take the form of respective capacitor banks capable of storing up to 100-200 kJ or 3-4 MJ, for example.

The plasma confinement system200includes an assembly region226within the outer electrode204between the first end218of the inner electrode202and the first end222of the outer electrode204. The plasma confinement system200is configured to sustain a Z-pinch plasma within the assembly region226as described below.

The plasma confinement system200also includes a gas source230(e.g., a pressurized gas tank) and one or more first regulators232configured to control gas flow from the gas source230through the respective one or more first valves206. Connections (e.g., piping) between the one or more first regulators232and the one or more first valves206are omitted inFIG.2for clarity.

The plasma confinement system200also includes two or more second regulators234configured to control gas flow from the gas source230through the respective two or more second valves212. Connections (e.g., piping) between the two or more second regulators234and the two or more second valves212are omitted inFIG.2for clarity.

The plasma confinement system200also includes a first insulator236between the second end224of the outer electrode204and the intermediate electrode203. The first insulator236generally has an annular cross section.

The plasma confinement system200also includes a second insulator237between the second end221of the intermediate electrode203and the inner electrode202. The second insulator237generally has an annular cross section.

The plasma confinement system200also includes a vacuum chamber238(e.g., a steel vessel) that at least partially surrounds the inner electrode202, the intermediate electrode203, and the outer electrode204, as shown inFIG.2.

FIG.3is a schematic cross-sectional diagram of a plasma confinement system300. The plasma confinement system300includes an inner electrode302, an outer electrode304that substantially surrounds the inner electrode302, and an intermediate electrode303that faces the inner electrode302. The plasma confinement system300also includes one or more first valves306configured to direct gas from within the inner electrode302to an acceleration region310between the inner electrode302and the outer electrode304and two or more second valves312configured to direct gas from outside the outer electrode304to the acceleration region310. The plasma confinement system300also includes a first power supply314configured to apply a voltage between the inner electrode302and the outer electrode304and a second power supply315configured to apply a voltage between the inner electrode302and the intermediate electrode303.

The inner electrode302generally takes the form of an electrically conducting (e.g., stainless steel) shell having a substantially cylindrical body316. The inner electrode302includes a first end318(e.g. a rounded end) and an opposing second end320(e.g., a substantially circular end). More specifically, the first end318may have a conical shape with a rounded tip. The inner electrode302is generally similar to the inner electrode102and the inner electrode202discussed above. The inner electrode302may include one or more conduits or channels (not labeled) for routing gas from the one or more first valves306to the acceleration region310.

The outer electrode304also generally takes the form of an electrically conducting (e.g., stainless steel) shell having a substantially cylindrical body328. The first end322of the outer electrode304is substantially circular and the second end324of the outer electrode is substantially circular. The outer electrode304surrounds much of the inner electrode302. The inner electrode302and the outer electrode304may be concentric and have radial symmetry with respect to the same axis. The first end318of the inner electrode302is between the first end322of the outer electrode304and the second end324of the outer electrode304. The outer electrode304may include one or more conduits or channels (not shown) for routing gas from the two or more second valves312to the acceleration region310.

The intermediate electrode303also generally takes the form of an electrically conducting material (e.g., stainless steel) and is substantially disc-shaped.

The one or more first valves306may take the form of “puff valves,” but may include any type of valve configured to direct gas (e.g., hydrogen or deuterium) from within the inner electrode302to an acceleration region310between the inner electrode302and the outer electrode304. As shown inFIG.3, the one or more first valves306are positioned axially between the first end318of the inner electrode302and the second end320of the inner electrode302. Alternatively, the one or more first valves might be located at the first end318or the second end320of the inner electrode302. InFIG.3, the one or more first valves306are positioned within the inner electrode302, but other examples are possible. The one or more first valves306can be operated by providing the one or more first valves306with a control voltage, as described below.

The acceleration region310has a substantially annular cross section defined by the shapes of the inner electrode302and the outer electrode304.

The two or more second valves312may take the form of “puff valves,” but may include any type of valve configured to direct gas (e.g., hydrogen or deuterium) from outside the outer electrode304to the acceleration region310. As shown inFIG.3, the two or more second valves312are positioned axially between the first end322of the outer electrode304and the second end324of the outer electrode304. Alternatively, the two or more second valves may be located at the second end324or at the first end322. The two or more second valves312will generally be arranged around (e.g., outside of) the outer electrode304. As shown inFIG.3, the one or more first valves306are axially aligned with the two or more second valves312, but other examples are possible. The two or more second valves312can be operated by providing the two or more second valves312with a control voltage, as described below.

The first power supply314and the second power supply315will generally take the form of respective capacitor banks capable of storing up to 100-200 kJ or 3-4 MJ, for example.

The plasma confinement system300includes an assembly region326within the outer electrode304between the first end318of the inner electrode302and the intermediate electrode303. The plasma confinement system300is configured to sustain a Z-pinch plasma within the assembly region326as described below.

The plasma confinement system300also includes a gas source330(e.g., a pressurized gas tank) and one or more first regulators332configured to control gas flow from the gas source330through the respective one or more first valves306. Connections (e.g., piping) between the one or more first regulators332and the one or more first valves306are omitted inFIG.3for clarity.

The plasma confinement system300also includes two or more second regulators334configured to control gas flow from the gas source330through the respective two or more second valves312. Connections (e.g., piping) between the one or more second regulators334and the two or more second valves312are omitted inFIG.3for clarity.

The plasma confinement system300also includes a first insulator336(e.g., having an annular cross section) between the outer electrode304and the inner electrode302to maintain electrical isolation between the inner electrode302and the outer electrode304.

The plasma confinement system300also includes a second insulator337(e.g., having an annular cross section) between the second end322of the outer electrode304and the intermediate electrode303to maintain electrical isolation between the intermediate electrode303and the outer electrode304.

The plasma confinement system300also includes a vacuum chamber338that at least partially surrounds the inner electrode302, the intermediate electrode303, and/or the outer electrode304.

FIG.4is a block diagram of a method400for operating a plasma confinement system (e.g., the plasma confinement system100).FIGS.1,5A-F,6, and7viewed together illustrate some of the aspects of the method400as described below.FIGS.5A-Finclude simplified diagrams of portions of the plasma confinement system100as well as depict functionality of the plasma confinement system100.

At block402, the method400includes directing gas, via one or more first valves, from within an inner electrode to an acceleration region between the inner electrode and an outer electrode that substantially surrounds the inner electrode.

For example, the one or more first valves106may direct gas412(seeFIGS.5A-B), from within the inner electrode102to the acceleration region110between the inner electrode102and the outer electrode104that substantially surrounds the inner electrode102.FIG.5Ashows an initial amount of the gas412entering the acceleration region110andFIG.5Bshows an additional amount of the gas412entering the acceleration region110.

FIG.6depicts some other possible features of the method400. Voltages, waveforms, and times depicted inFIG.6are not necessarily shown to scale. In some embodiments, directing the gas412via the one or more first valves106includes providing (via a power supply such as a capacitor bank that is not shown) a first valve voltage420to the one or more first valves106(e.g., to control terminals of the one or more first valves106) followed by providing a second valve voltage422(e.g., via a DC power supply) to the one or more first valves106.

In this context, the first valve voltage420is generally within a range of 270 to 330 volts, within a range of 290 to 310 volts, or within a range of 295 to 305 volts. Voltages recited herein are generally DC voltages unless otherwise specified. The first valve voltage420may be provided for a duration424within a range of 90 to 110 μs, within a range of 95 to 105 μs, or within a range of 98 to 102 μs. It should be noted that the respective waveforms of the first valve voltage420and the second valve voltage422in practice will not take the form of square waves, but will generally have a smoother waveform and transition between the first valve voltage420and the second valve voltage422characteristic of an RLC circuit.

The second valve voltage422might be within a range of 13.5 to 16.5 volts, within a range of 14 to 16 volts, or within a range of 14.5 to 15.5 volts. For example, the second valve voltage422might be provided for a duration426within a range of 0.5 to 5 ms, within a range of 0.65 to 3.5 ms, or within a range of 0.75 to 2 ms. Typically the first valve voltage420is greater than the second valve voltage422and the second valve voltage422is provided immediately after providing the first valve voltage420.

After operation of the one or more first valves106, a gas pressure428(seeFIG.7) adjacent to the one or more first valves106might be within a range of 1000 to 5800 Torr (e.g., 5450 to 5550 Torr) prior to the voltage414(seeFIG.6) between the inner electrode102and the outer electrode104being applied via the power supply114.

Directing the gas412via the one or more first valves106might include opening the one or more first valves106for a duration within a range of 1.1 to 2 milliseconds (ms) or within a range of 1.3 to 1.5 ms. Additionally, directing the gas412via the one or more first valves106might include opening the one or more first valves1061.0 to 1.6 ms or 1.3 to 1.5 ms prior to applying the voltage414between the inner electrode102and the outer electrode104via the power supply114.

At block404, the method400includes directing gas, via two or more second valves, from outside the outer electrode to the acceleration region. For example, the two or more second valves112may direct a portion of the gas412into the acceleration region110as shown inFIGS.5A-B.

In some embodiments, directing the gas412via the two or more second valves112includes providing (via a power supply such as a capacitor bank that is not shown) a third valve voltage430(seeFIG.6) to the two or more second valves112(e.g., to control terminals of the two or more second valves112) followed by providing a fourth valve voltage432(e.g., via a DC power supply) to the two or more second valves112.

In this context, the third valve voltage430is generally within a range of 270 to 330 volts, within a range of 290 to 310 volts, or within a range of 295 to 305 volts. The third valve voltage430might be provided for a duration434within a range of 90 to 110 μs, within a range of 95 to 105 μs, or within a range of 98 to 102 μs. It should be noted that the respective waveforms of the third valve voltage430and the fourth valve voltage432in practice will not take the form of square waves, but will generally have a smoother waveform and transition between the third valve voltage430and the fourth valve voltage432characteristic of an RLC circuit.

The fourth valve voltage432is generally within a range of 13.5 to 16.5 volts, within a range of 14 to 16 volts, or within a range of 14.5 to 15.5 volts. The fourth valve voltage432might be provided for a duration436within a range of 0.5 to 5 ms, within a range of 0.65 to 3.5 ms, or within a range of 0.75 to 2 ms. The third valve voltage430is typically greater than the fourth valve voltage432. The fourth valve voltage432is generally provided immediately after providing the third valve voltage430.

After operation of the two or more second valves112, a gas pressure438(seeFIG.7) adjacent to the two or more second valves112might be within a range of 1000 to 5800 Torr (e.g., 5450 to 5550 Torr) prior to the voltage414between the inner electrode102and the outer electrode104being applied via the power supply114.

Directing the gas412via the two or more second valves112might include opening the two or more second valves112for a duration within a range of 0.75 to 1 milliseconds (ms) or within a range of 0.8 to 0.95 ms.

Additionally, directing the gas412via the two or more second valves112might include opening the two or more second valves1120.6 to 1.2 ms or 0.7 to 0.9 ms prior to applying the voltage414between the inner electrode102and the outer electrode104via the power supply114.

After operation of the one or more first valves106and the two or more second valves112, a gas pressure440(seeFIG.7) within the acceleration region110might be within a range of 1000 to 5800 Torr (e.g., 5450 to 5550 Torr) prior to the voltage414between the inner electrode102and the outer electrode104being applied via the power supply114. The gas pressure within the acceleration region will generally decrease with increasing distance from the point of gas insertion and with the passage of time after gas is no longer introduced to the acceleration region.

At block406, the method400includes applying, via a power supply, a voltage between the inner electrode and the outer electrode, thereby converting at least a portion of the directed gas into a plasma having a substantially annular cross section, the plasma flowing axially within the acceleration region toward a first end of the inner electrode and a first end of the outer electrode and, thereafter, establishing a Z-pinch plasma that flows between the first end of the outer electrode and the first end of the inner electrode.

For example, the power supply114might apply the voltage414between the inner electrode102and the outer electrode104, thereby converting at least a portion of the directed gas412into a plasma416(seeFIGS.5C-D) having a substantially annular cross section. Due to the magnetic field generated by its own current, the plasma416may flow axially within the acceleration region110toward the first end118of the inner electrode102and the first end122of the outer electrode104as shown inFIGS.5C-D. When the plasma416moves beyond the acceleration region110, a Z-pinch plasma418(seeFIGS.5E-F) is established and flows between the first end122of the outer electrode104and the first end118of the inner electrode102.

The Z-pinch plasma418generally flows in the assembly region126within the outer electrode104between the first end118of the inner electrode102and the first end122of the outer electrode104.

The voltage414applied by the power supply114between the inner electrode102and the outer electrode104might be within a range of 2 kV to 30 kV. The voltage414might be applied for a duration442(seeFIG.6) within a range of 50 to 400 μs.

The voltage414applied between the inner electrode102and the outer electrode104might result in a radial electric field within the acceleration region110within a range of 30 kV/m to 500 kV/m.

The Z-pinch plasma418may exhibit sheared axial flow and have a radius between 0.1 mm and 5 mm, an ion temperature between 900 and 2000 eV, an electron temperature greater than 500 eV, an ion number density greater than 1×1023ions/m3or an electron number density of greater than 1×1023electrons/m3, a magnetic field over 8 T, and/or may be stable for at least 10 μs.

FIG.8is a block diagram of a method800for operating a plasma confinement system (e.g., the plasma confinement system200).FIGS.2,9A-F,10, and11viewed together illustrate some of the aspects of the method800as described below.FIGS.9A-Finclude simplified diagrams of portions of the plasma confinement system200as well as depict functionality of the plasma confinement system200.

At block802, the method800includes directing gas, via one or more first valves, from within an inner electrode to an acceleration region between the inner electrode and an intermediate electrode that substantially surrounds the inner electrode.

For example, the one or more first valves206may direct gas812from within the inner electrode202to an acceleration region210between the inner electrode202and the intermediate electrode203that substantially surrounds the inner electrode202.FIG.9Ashows an initial amount of the gas812entering the acceleration region210andFIG.9Bshows an additional amount of the gas812entering the acceleration region210.

FIG.10depicts some other possible features of the method800. Voltages, waveforms, and times depicted inFIG.10are not necessarily shown to scale. In some embodiments, directing the gas812via the one or more first valves206includes providing (via a power supply such as a capacitor bank that is not shown) a first valve voltage820to the one or more first valves206(e.g., to control terminals of the one or more first valves206) followed by providing a second valve voltage822(e.g., via a DC power supply) to the one or more first valves206.

In this context, the first valve voltage820is generally within a range of 270 to 330 volts, within a range of 290 to 310 volts, or within a range of 295 to 305 volts. Voltages recited herein are DC voltages unless otherwise specified. The first valve voltage820may be provided for a duration824within a range of 90 to 110 μs, within a range of 95 to 105 μs, or within a range of 98 to 102 μs. It should be noted that the respective waveforms of the first valve voltage820and the second valve voltage822in practice will not take the form of square waves, but will generally have a smoother waveform and transition between the first valve voltage820and the second valve voltage822characteristic of an RLC circuit.

The second valve voltage822might be within a range of 13.5 to 16.5 volts, within a range of 14 to 16 volts, or within a range of 14.5 to 15.5 volts. For example, the second valve voltage822might be provided for a duration826within a range of 0.5 to 5 ms, within a range of 0.65 to 3.5 ms, or within a range of 0.75 to 2 ms. Typically the first valve voltage820is greater than the second valve voltage822and the second valve voltage822is provided immediately after providing the first valve voltage820.

After operation of the one or more first valves206, a gas pressure828(seeFIG.11) adjacent to the one or more first valves206might be within a range of 1000 to 5800 Torr (e.g., 5450 to 5550 Torr) prior to the voltage814(seeFIG.10) between the inner electrode202and the intermediate electrode203being applied via the power supply214.

Directing the gas812via the one or more first valves206might include opening the one or more first valves206for a duration within a range of 1.1 to 2 milliseconds (ms) or within a range of 1.3 to 1.5 ms. Additionally, directing the gas812via the one or more first valves206might include opening the one or more first valves2061.0 to 1.6 ms or 1.3 to 1.5 ms prior to applying the voltage814between the inner electrode202and the intermediate electrode203via the power supply214.

At block804, the method800includes directing gas, via two or more second valves, from outside the intermediate electrode to the acceleration region. For example, the two or more second valves212may direct a portion of the gas812into the acceleration region210as shown inFIGS.9A-B.

In some embodiments, directing the gas812via the two or more second valves212includes providing (via a power supply such as a capacitor bank that is not shown) a third valve voltage830to the two or more second valves212(e.g., to control terminals of the two or more second valves212) followed by providing a fourth valve voltage832(e.g., via a DC power supply) to the two or more second valves212.

In this context, the third valve voltage830is generally within a range of 270 to 330 volts, within a range of 290 to 310 volts, or within a range of 295 to 305 volts. The third valve voltage830might be provided for a duration834within a range of 90 to 110 μs, within a range of 95 to 105 μs, or within a range of 98 to 102 μs. It should be noted that the respective waveforms of the third valve voltage830and the fourth valve voltage832in practice will not take the form of square waves, but will generally have a smoother waveform and transition between the third valve voltage830and the fourth valve voltage832characteristic of an RLC circuit.

The fourth valve voltage832is generally within a range of 13.5 to 16.5 volts, within a range of 14 to 16 volts, or within a range of 14.5 to 15.5 volts. The fourth valve voltage832might be provided for a duration836within a range of 0.5 to 5 ms, within a range of 0.65 to 3.5 ms, or within a range of 0.75 to 2 ms. The third valve voltage830is typically greater than the fourth valve voltage832. The fourth valve voltage832is generally provided immediately after providing the third valve voltage830.

After operation of the two or more second valves212, a gas pressure838(seeFIG.11) adjacent to the two or more second valves212might be within a range of 1000 to 5800 Torr (e.g., 5450 to 5550 Torr) prior to the voltage814between the inner electrode202and the intermediate electrode203being applied via the power supply214.

Directing the gas812via the two or more second valves212might include opening the two or more second valves212for a duration within a range of 0.75 to 1 milliseconds (ms) or within a range of 0.8 to 0.95 ms.

Additionally, directing the gas812via the two or more second valves212might include opening the two or more second valves2120.6 to 1.2 ms or 0.7 to 0.9 ms prior to applying the voltage814between the inner electrode202and the intermediate electrode203via the power supply214.

After operation of the one or more first valves206and the two or more second valves212, a gas pressure840(seeFIG.11) within the acceleration region210might be within a range of 1000 to 5800 Torr (e.g., 5450 to 5550 Torr) prior to the voltage814between the inner electrode102and the intermediate electrode203being applied via the power supply214. The gas pressure within the acceleration region will generally decrease with increasing distance from the point of gas insertion and with the passage of time after gas is no longer introduced to the acceleration region.

At block806, the method800includes applying, via a first power supply, a voltage between the inner electrode and the intermediate electrode, thereby converting at least a portion of the directed gas into a plasma having a substantially annular cross section, the plasma flowing axially within the acceleration region toward a first end of the inner electrode and a first end of the outer electrode.

For example, the first power supply214may apply the voltage814(seeFIG.10) between the inner electrode202and the intermediate electrode203, thereby converting at least a portion of the directed gas812into a plasma816(seeFIGS.9C-D) having a substantially annular cross section. Due to the magnetic field generated by its own current, the plasma816may flow axially within the acceleration region210toward the first end218of the inner electrode202and the first end222of the outer electrode204as shown inFIGS.9C-D.

The voltage814applied by the power supply214between the inner electrode202and the intermediate electrode203might be within a range of 2 kV to 30 kV. The voltage814might be applied for a duration842(seeFIG.10) within a range of 50 to 400 μs.

The voltage814applied between the inner electrode202and the intermediate electrode203might result in a radial electric field within the acceleration region210within a range of 30 kV/m to 500 kV/m.

At block808, the method800includes applying, via a second power supply, a voltage between the inner electrode and the outer electrode to establish a Z-pinch plasma that flows between the first end of the outer electrode and the first end of the inner electrode.

For example, the second power supply215might apply a voltage815(seeFIG.10) between the inner electrode202and the outer electrode204to establish a Z-pinch plasma818(seeFIGS.9E-F) that flows between the first end222of the outer electrode204and the first end218of the inner electrode202. When the plasma816moves beyond the acceleration region210, the Z-pinch plasma818is established in the assembly region226within the outer electrode204between the first end218of the inner electrode202and the first end222of the outer electrode204.

It should be noted that blocks806and808might also be implemented by other means of controlling (a) the voltage between the inner electrode202and the intermediate electrode203and (b) the voltage between the intermediate electrode203and the outer electrode204, as one of skill in the art will recognize. For example, a power supply might provide a voltage between the intermediate electrode203and the outer electrode204, instead of between the inner electrode and the outer electrode.

Applying the voltage between the inner electrode202and the outer electrode204might include commencing applying the voltage between the inner electrode202and the outer electrode20417-27 μs or 19-22 μs after commencing applying the voltage between the inner electrode202and the intermediate electrode203.

The voltage815applied by the power supply215between the inner electrode202and the outer electrode204is generally within a range of 2 kV to 30 kV. The voltage815might be applied for a duration844within a range of 50-400 μs.

The Z-pinch plasma818may exhibit sheared axial flow and have a radius between 0.1 mm and 5 mm, an ion temperature between 900 and 2000 eV, an electron temperature greater than 500 eV, an ion number density greater than 1×1023ions/m3or an electron number density of greater than 1×1023electrons/m3, a magnetic field over 8 T, and/or may be stable for at least 10 μs.

FIG.12is a block diagram of a method900for operating a plasma confinement system (e.g., the plasma confinement system300).FIGS.3,13A-F,14, and15viewed together illustrate some of the aspects of the method900as described below.FIGS.13A-Finclude simplified diagrams of portions of the plasma confinement system300as well as depict functionality of the plasma confinement system300.

At block902, the method900includes directing gas, via one or more first valves, from within an inner electrode to an acceleration region between the inner electrode and an outer electrode that substantially surrounds the inner electrode.

For example, the one or more first valves306may direct gas912(seeFIGS.13A-B), from within the inner electrode302to the acceleration region310between the inner electrode302and the outer electrode304that substantially surrounds the inner electrode302.FIG.13Ashows an initial amount of the gas912entering the acceleration region310andFIG.13Bshows an additional amount of the gas912entering the acceleration region310.

FIG.14depicts some other possible features of the method900. Voltages, waveforms, and times depicted inFIG.14are not necessarily shown to scale. In some embodiments, directing the gas912via the one or more first valves306includes providing (via a power supply such as a capacitor bank that is not shown) a first valve voltage920to the one or more first valves306(e.g., to control terminals of the one or more first valves306) followed by providing a second valve voltage922(e.g., via a DC power supply) to the one or more first valves306.

In this context, the first valve voltage920is generally within a range of 270 to 330 volts, within a range of 290 to 310 volts, or within a range of 295 to 305 volts. Voltages recited herein are generally DC voltages unless otherwise specified. The first valve voltage920may be provided for a duration924within a range of 90 to 110 μs, within a range of 95 to 105 μs, or within a range of 98 to 102 μs. It should be noted that the respective waveforms of the first valve voltage920and the second valve voltage922in practice will not take the form of square waves, but will generally have a smoother waveform and transition between the first valve voltage920and the second valve voltage922characteristic of an RLC circuit.

The second valve voltage922might be within a range of 13.5 to 16.5 volts, within a range of 14 to 16 volts, or within a range of 14.5 to 15.5 volts. For example, the second valve voltage922might be provided for a duration926within a range of 0.5 to 5 ms, within a range of 0.65 to 3.5 ms, or within a range of 0.75 to 2 ms. Typically the first valve voltage920is greater than the second valve voltage922and the second valve voltage922is provided immediately after providing the first valve voltage920.

After operation of the one or more first valves306, a gas pressure928(seeFIG.15) adjacent to the one or more first valves306might be within a range of 1000 to 5800 Torr (e.g., 5450 to 5550 Torr) prior to the voltage914(seeFIG.14) between the inner electrode302and the outer electrode304being applied via the power supply314.

Directing the gas912via the one or more first valves306might include opening the one or more first valves306for a duration within a range of 1.1 to 2 milliseconds (ms) or within a range of 1.3 to 1.5 ms. Additionally, directing the gas912via the one or more first valves306might include opening the one or more first valves3061.0 to 1.6 ms or 1.3 to 1.5 ms prior to applying the voltage914between the inner electrode302and the outer electrode304via the power supply314.

At block904, the method900includes directing gas, via two or more second valves, from outside the outer electrode to the acceleration region. For example, the two or more second valves312may direct a portion of the gas912into the acceleration region310as shown inFIGS.13A-B.

In some embodiments, directing the gas912via the two or more second valves312includes providing (via a power supply such as a capacitor that is not shown) a third valve voltage930(seeFIG.14) to the two or more second valves312(e.g., to control terminals of the two or more second valves312) followed by providing a fourth valve voltage932(e.g., via a DC power supply) to the two or more second valves312.

In this context, the third valve voltage930is generally within a range of 270 to 330 volts, within a range of 290 to 310 volts, or within a range of 295 to 305 volts. The third valve voltage930might be provided for a duration934within a range of 90 to 110 μs, within a range of 95 to 105 μs, or within a range of 98 to 102 μs. It should be noted that the respective waveforms of the third valve voltage930and the fourth valve voltage932in practice will not take the form of square waves, but will generally have a smoother waveform and transition between the third valve voltage930and the fourth valve voltage932characteristic of an RLC circuit.

The fourth valve voltage932is generally within a range of 13.5 to 16.5 volts, within a range of 14 to 16 volts, or within a range of 14.5 to 15.5 volts. The fourth valve voltage932might be provided for a duration936within a range of 0.5 to 5 ms, within a range of 0.65 to 3.5 ms, or within a range of 0.75 to 2 ms. The third valve voltage930is typically greater than the fourth valve voltage932. The fourth valve voltage932is generally provided immediately after providing the third valve voltage930.

After operation of the two or more second valves312, a gas pressure938(seeFIG.15) adjacent to the two or more second valves312might be within a range of 1000 to 5800 Torr (e.g., 5450 to 5550 Torr) prior to the voltage914between the inner electrode302and the outer electrode304being applied via the power supply314.

Directing the gas912via the two or more second valves312might include opening the two or more second valves312for a duration within a range of 0.75 to 1 milliseconds (ms) or within a range of 0.8 to 0.95 ms.

Additionally, directing the gas912via the two or more second valves312might include opening the two or more second valves3120.6 to 1.2 ms or 0.7 to 0.9 ms prior to applying the voltage914between the inner electrode302and the outer electrode304via the power supply314.

After operation of the one or more first valves306and the two or more second valves312, a gas pressure940(seeFIG.15) within the acceleration region310might be within a range of 1000 to 5800 Torr (e.g., 5450 to 5550 Torr) prior to the voltage914between the inner electrode302and the outer electrode304being applied via the power supply314. The gas pressure within the acceleration region will generally decrease with increasing distance from the point of gas insertion and with the passage of time after gas is no longer introduced to the acceleration region.

At block906, the method900includes applying, via a first power supply, a voltage between the inner electrode and the outer electrode, thereby converting at least a portion of the directed gas into a plasma having a substantially annular cross section, the plasma flowing axially within the acceleration region toward a first end of the inner electrode and a first end of the outer electrode.

For example, the power supply314might apply the voltage914between the inner electrode302and the outer electrode304, thereby converting at least a portion of the directed gas912into a plasma916(seeFIGS.13C-D) having a substantially annular cross section. Due to the magnetic field generated by its own current, the plasma916may flow axially within the acceleration region310toward the first end318of the inner electrode302and the first end322of the outer electrode304as shown inFIGS.13C-D.

The voltage914applied by the power supply314between the inner electrode302and the outer electrode304might be within a range of 2 kV to 30 kV. The voltage914might be applied for a duration942(seeFIG.14) within a range of 50 to 400 μs.

The voltage914applied between the inner electrode302and the outer electrode304might result in a radial electric field within the acceleration region310within a range of 30 kV/m to 500 kV/m.

At block908, the method900includes applying, via a second power supply, a voltage between the inner electrode and an intermediate electrode to establish a Z-pinch plasma that flows between the intermediate electrode and the first end of the inner electrode. In this context, the intermediate electrode is positioned at a first end of the outer electrode.

For example, the power supply315might apply a voltage915between the inner electrode302and an intermediate electrode303to establish a Z-pinch plasma918that flows between the intermediate electrode303and the first end318of the inner electrode302. The Z-pinch plasma918is established when the plasma916moves beyond the acceleration region310. The Z-pinch plasma918flows in the assembly region326within the outer electrode304between the first end318of the inner electrode302and the intermediate electrode303.

Applying the voltage between the inner electrode302and the intermediate electrode303might include commencing applying the voltage between the inner electrode302and the intermediate electrode30317-27 μs or 19-22 μs after commencing applying the voltage between the inner electrode302and the outer electrode304.

It should be noted that blocks906and908might also be implemented by other means of controlling (a) the voltage between the inner electrode302and the outer electrode304and (b) the voltage between the inner electrode302and the intermediate electrode303, as one of skill in the art will recognize. For example, a power supply might provide a voltage between the intermediate electrode303and the outer electrode304, instead of between the inner electrode and the intermediate electrode. The voltage915applied by the power supply315between the inner electrode102and the intermediate electrode303might be within a range of 2 kV to 30 kV. The voltage915might be applied for a duration942(seeFIG.14) within a range of 50 to 400 μs.

The Z-pinch plasma918may exhibit sheared axial flow and have a radius between 0.1 mm and 5 mm, an ion temperature between 900 and 2000 eV, an electron temperature greater than 500 eV, an ion number density greater than 1×1023ions/m3or an electron number density of greater than 1×1023electrons/m3, a magnetic field over 8 T, and/or may be stable for at least 10 μs.

While various example aspects and example embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in the art. The various example aspects and example embodiments disclosed herein are for purposes of illustration and are not intended to be limiting, with the true scope and spirit being indicated by the following claims.