The high azimuthal magnetic field of a current-carrying plasma column (z-pinch) can be used to collect and focus high-energy charged particles in accelerators The beam optics and the apparent advantages of such a linear lens compared with conventional focusing devices, such as magnets and magnetic horns, are described When a plasma lens shall be operated in routine accelerator runs, the physics of the plasma dynamics must be largely understood and the technology has to be mastered The results of plasma dynamics measurements and of long-term behavior tests with a plasma lens for antiproton collection are reported The problems of the plasma dynamics control and of the plasma-wall interaction are discussed in view of the envisaged performance for antiproton collection

/pdf/a-z-pinch-plasma-lens-for-focusing-high-energy-particles-in-k3i0ibnjis.pdf

A Z-Pinch Plasma Lens for Focusing High-Energy Particles in an Accelerator

The high azimuthal magnetic field of a current-carrying plasma column (z-pinch) can be used to collect and focus high-energy charged particles in accelerators. The beam optics and the apparent advantages of such a linear lens compared with conventional focusing devices, such as magnets and magnetic horns, are described. When a plasma lens shall be operated in routine accelerator runs, the physics of the plasma dynamics must be largely understood and the technology has to be mastered. The results of plasma dynamics measurements and of long-term behavior tests with a plasma lens for antiproton collection are reported. The problems of the plasma dynamics control and of the plasma-wall interaction are discussed in view of the envisaged performance for antiproton collection.

/pdf/a-z-pinch-plasma-lens-for-focusing-high-energy-particles-in-4ehkhbn7gj.pdf

A Z-pinch plasma lens for focusing high-energy particles in an accelerator (CERN-PS-88-34-AR)

The dynamical formation of a Z-pinch in the strong-shock limit is studied in this paper using one-dimensional (1D) simulations of a two-temperature magnetohydrodynamic model. The classic 1D picture consists of three stages: run-in, reflected-shock, and expansion. The special case of a constant current I and uniform gas fill, which are approximate conditions of the pinch-formation stage in a dense plasma focus, is examined in detail. Time-profiles for the shock-front and piston positions during the run-in stage are compared with some of the commonly used 0D models from the literature. Some practical improvements to these models are presented here and it is shown that this model gives the best agreement with results from the simulations. Maximum compression of the plasma is achieved when the reflected shock from the axis meets the incoming current layer. The ratio of the plasma radius at this time with respect to its initial radius is found from the simulations to be r p / R ≈ 1 / 8 using 5/3 for the adiabatic coefficient γ. The pressure and temperature of the compressed plasma are found to peak a short time after maximum compression due to the inability of the reflected shock to completely stagnate the incoming plasma driven by the converging current layer. The variation of the results with a finite dI/dt and for different values of γ is presented.

One-dimensional theory and simulations of the dynamic Z-pinch

In this chapter we review numerical experiments using the Lee Model code. We describe the contributions made by this code in the past 30 years in the light of overall work on simulations already documented in the area of plasma focus. The plasma focus exhibits interesting phenomena ranging from electromagnetically driven dynamics to copious radiation including ions, electrons, X-rays, characteristic soft X-rays, fusion neutrons, to fast ion beams (FIB) and fast plasma streams (FPS), to anomalous resistivity resulting from a range of plasma instabilities, to plasma states of extreme high-energy density (HED) achieved through radiative cooling and collapse. The Lee Model code is successful in modelling many of these multi-faceted aspects of the plasma focus. The physics, equations and contributions of the code are explained in this chapter. Its success on so many fronts is attributed to its use of 4 parameters (fitted to a measured current waveform) which in one sweep incorporates all the mechanisms and effects occurring in the plasma focus including mechanisms and effects difficult to compute or even as yet unrecognized. The simple premise is that the sum total effect of all these mechanisms and phenomena is represented in net result by mass field and force field distributions which in the gross sense are represented by a mass swept-up factor f m and an effective current factor f c in the axial phase and two corresponding factors in the radial phase, up to the end of the focus pinch. Once matched, the fitted model parameters assure that the computation proceeds with all physical mechanisms accounted for, at least in the gross energy and mass balance sense.

The Plasma Focus—Numerical Experiments, Insights and Applications

The most probable initial magnetic configuration of a CME is a flux rope consisting of twisted field lines which fill the whole volume of a dark coronal cavity. The flux ropes can be in stable equilibrium in the coronal magnetic field for weeks and even months, but suddenly they loose their stability and erupt with high speed. Their transition to the unstable phase depends on the parameters of the flux rope (i.e., total electric current, twist, mass loading etc.), as well as on the properties of the ambient coronal magnetic field. One of the major governing factors is the vertical gradient of the coronal magnetic field which is estimated as decay index (n). Cold dense prominence material can be collected in the lower parts of the helical flux tubes. Filaments are therefore good tracers of the flux ropes in the corona, which become visible long before the beginning of the eruption. The perspectives of the filament eruptions and following CMEs can be estimated by the comparison of observed filament heights with calculated decay index distributions. The present paper reviews the formation of magnetic flux ropes, their stable and unstable phases, eruption conditions, and also discusses their physical implications in the solar corona.

Solar Magnetic Flux Ropes

A general model is adopted with the magnetic piston perfectly coupled to the imploding plasma. The work done by the piston in moving from initial radius r0 to equilibrium radius rp is equated to the enthalpy of the plasma column at rp. This, together with pressure balance, suffices to produce an expression for the pinch ratio dependent only on gamma , the specific heat ratio of the pinched plasma. For a constant current, constant length pinch with gamma =5/3 a pinch ratio of 0.29 is predicted. For the pinch phase of a gamma =5/3 plasma focus treated as a constant current pinch having a length which increases with decreasing radius, a pinch ratio of 0.14 is predicted. These compare well with experimentally observed values.

https://iopscience.iop.org/article/10.1088/0032-1028/25/5/009/pdf

Energy balance and the radius of electromagnetically pinched plasma columns

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Energy balance and the radius of electromagnetically pinched plasma columns