Pulsed Power Plasmas

 

Pulsed power is simply the compression of electrical energy into short, high power bursts. This typically uses capacitive storage charged slowly from a wall outlet, which is then discharged in timescales from nanoseconds to milliseconds through a target. This method can be used to initialize and drive plasmas in solids, liquids and gases, and has found applications in areas from water sanitation to x-ray lasers and inertial confinement fusion.

 

 

Wire-based Z-Pinches

In the P³ group our primary targets are fine metallic wires (e.g. Al, Cu or W) which can be loaded in various geometries depending on the experiment of interest. Wire diameters are typically 5 to 50 microns in diameter and are strung between two electrodes. For most experiments the drive current is 100 kA to several MA and rises to a maximum in around 100 - 300 ns. For a single wire, this axial current initially ohmically heats the material which expands outwards at the sound speed. At the current rises the self-generated azimuthal magnetic field increases rapidly and pinches the plasma back onto its axis through the Lorentz (j x B) force. In this geometry the process is refered to as a z-pinch, since the current flows along the axial, or z, axis. As pinching occurs, the interface of the plasma and the B-field is highly unstable to magneto-hydrodynamics (MHD) and a classical classical m=0 structure is observed.

Wire array z-pinches comprise a cylindrical arrangement of metal wires, and can use as few as 4 wires on smaller generator and several hundred wires on ther largest. This arrangement means there is both a B-field generated around each wire ('local' to the wire) and a B-field around the entire array (referred to as 'global')since the current flow is in the same direction in each wire. This global B-field causes the array to collapse onto its axis, creating a high power soft x-ray burst. The largest pulsed power generator in the world is called "Z", and is based at Sandia National Laboratories. This produces 26MA in 100ns, and it the most powerful laboratory x-ray source, generating 1.8 MJ of x-ray energy at a power of 280 TW, and is a potential driver for both Inertial Confinement Fusion (ICF) and Inertial Fusion Energy (IFE) [2].

 

Wire array z-pinches are a complex plasma system, and produce a wide range of plasma parameters throughout their evolution. The experiment can typically be broken down into 4 identifiable stages:

 

 

 

1) Wire inititation 
2) Ablation phase 
3) Implosion phase 
4) Stagnation and x-ray generation
 

 

 

 

The high voltage from the pulsed power generator (100kV to several MV) initiates the array by rapidly causing electrical breakdown at the wire surface, forming a plasma in a few nanoseconds. At this point each wire forms an heterogeneous plamsma structure referred to as the core-corona model. A cold dense wire core is surrounded by a hot low density coronal plasma. Due to the greater volume and higher ionisation (an hence conductivity) of the corona, it is this plasma which carried much of the current and hence is accelerated towards the array axis. During the ablation phase, which can last for up to 80% of the experiment, the cores remain stationary and replenish the coronal material as it is removed by the Lorentz force [3].The rate at which mass is ablated from the wires typically scales as I2 [4], and this determines the density of both the ablated plasma streams and subsequent structures formed interior to the array as these 'jets' converge onto the array axis [5, 6].

The stream densities produced in experiments have ion densities in the range of 1x10^14 - 5x10^17 cm-3, typically with temperatures 5-15 eV and Mach numbers between 3 and 5. Streams at current of 1 MA are typically collisional on the order of the array diameter (~8 mm), and form shock structures observable in emission images around objects place in their path, such as occurs in nested wire array experiments [7].

Eventually enough mass has been ablated from the wires that they begin to break, and this triggers the implosion phase. The JxB force accelerates much of the array mass towards the axis at velocities of 300 km/s, as can be deduced from the change in array diameter observed on radial streak camera images

 

The magnetic piston snow ploughs up the pre-fill plasma which serves to stabilize the implosion surface. Thestagnation of this mass at the array axis converts kinetic energy into thermal energy and this, along with additional heating from the plasma compression by the magnetic field, is radiated as a short (< 10ns) high power x-ray pulse. A time slice at stagnation form a 3D Magneto-Hydrodynamic simulation using the GORGON code [8], and example x-ray data is given below from the Z machine at Sandia National Laboratories (Ref [9])

For different applications, the geometry of the wires can be altered very simply, which changes the geometry of the driving B-fields [10]. Inclining the wires into a cone generates a central plasma column with axial momentum, which is then launched out of the array as a jet relevant to astrophysical jets. Using two rows, or planes, or wires generates two plasma columns (local to each plane), which can be caused to interact with each other later in the experiment. Inverting the electrode geometry causes a radially outward Lorentz force, and the plasma ejected can be used for studying shock formation in radiatively cooled flows (see Shocks project on the Projects page).

Pulsed power driven wire plasmas provide a versatile system to examine issues in laboratory astrophysics, basic plasma science and high energy density physics.

 

[1] J. P. Chittenden, et al, Phys. Rev. E, 61, 4370, (2000)
[2] M.E. Cuneo et al, Plasma Phys Control. Fusion, 48, R1 (2006) 
[3] S.V.Lebedev et al, Phys. Plasmas, 6, 2016, (1999) 
[4] S. Lebedev et al, Phys. Plasmas, 8, 3734, (2001)
[5] S.C.Bott et al, Phys Rev E, 74, 046403 (2006)
[6] S.C.Bott et al, IEEE Trans. Plasma Sci, 35, 165 (2007)
[7] D.J.Ampleford et al, Phys. Rev Lett., to be submitted
[8] J.P.Chittenden et al, Plasma Phys Control. Fusion, 46, B457 (2004)
[9] R.B.Spielman et al, Phys. Plasmas, 5, 2105, (1998)
[10] S.C.Bott et al, Phys. Rev. ST Accel. Beams, 14 , 050401 (2011)