Laboratory Astrophysics is the study of space plasma phenomena in the laboratory. Due to limitations in space, time and energy in laboratory experiments, it is only possible to study "model" of celestial objects. Our research focuses on magnetized or unmagnetized collimated plasma jets. They help us understand the formation and sustainment of plasma winds surrounded black holes and Herbig-Haro objects.

It is possible to extract relevant physical mechanism from our experiments by considering them as scale down versions of their larger, distant cousins. How is it even possible? In the same way as the physics allowing a model airplane to be airborne is the same as the one allowing a real airplane to fly, our experiments reproduce (barely) important parameters of space plasmas. We use radial foils as our platform of choice.

We turned to astrophysics to find out what parameters they think are important and we try to reach in our laboratory experiments. The most important parameters are the Reynolds number $$Re$$, the magnetic Reynolds number $$Re_M$$, the Péclet number $$Pe$$. The aspect ratio geometry as to be respected, in particular the ratio of the jet length to its diameter which should be above 10 to 100. The ratio of the jet particle density to the background density has to be at least 10.

The flows in accretion disks surrounding black holes, protostars and active galaxies are likely to be turbulently advective with significant magnetic fields. This implies $$Re >> 10^5$$, $$Re_M >> 10^3$$ and $$Pe >> 10^4$$. The $$Re$$ is the ratio of momentum density and scale length to viscous damping, the larger the more turbulent flows are. $$Re_M$$ is the ratio of plasma speed and scale length to its magnetic diffusivity. The larger it is the more magnetic fields are dragged by plasma flows. Finally $$Pe$$ is the ratio of plasma speed and scale length to its heat diffusivity. The larger the more flows advect heat. All these numbers are dimensionless (no mks unit) and apply to any plasma system, small or large. This is why plasmas in the lab can represent (or model) many astrophysical processes.

These parameters are strongly dependent of the state of the plasma and computing them requires compromises, the biggest one being that no one actually measured their values in space plasmas. Using classical plasma models we find that:

$$Re \propto Z^4A^{\frac{1}{2}}vLn_iT^{-\frac{5}{2}}$$, $$Re_M\propto Z^{-1}vLT^{\frac{3}{2}}$$, $$Pe \propto (Z+1)ZvLn_iT^{-\frac{5}{2}}$$

where $$Z$$ in the atomic number, $$A$$ is the atomic mass number, $$v$$ is the plasma velocity, $$L$$ is the plasma scale length, $$n_i$$ is the plasma ion density and $$T$$ is the plasma temperature. As one can see, it is not possible to obtain simultaneously large $$Re$$, $$Re_M$$ and $$Pe$$ by increasing the plasma temperature since the temperature dependance in $$Re_M$$ is weaker compared to the $$Re$$ and $$Pe$$. High temperatures may yield plasmas with large $$Re_M$$ but they will have little turbulence and heat advection. However the increase in plasma density $$n_i$$ as well as temperature will deliver simultaneously large $$Re$$, $$Re_M$$ and $$Pe$$. Of course using higher $$Z$$ and $$A$$ elements than hydrogen will help also.

This is why high energy density plasmas (HEDP) are at the forefront of laboratory astrophysics. This is a relatively new discipline which has been accepted by astrophysicists as a complementary step between numerical simulations and astrophysical observations. Ultimately only numerical codes can possibly encompass the sizes of most astrophysical objects and the art of numerical simulations does reside in finding the models which can best represent the phenomena observed by astrophysicists. In particular, laboratory experiments can help to validate these numerical codes. While kinetic effects cannot be ignored in astrophysical plasmas, today's large scale simulation efforts focus on the less computationally intensive fluid models. However the magnetohydrodynamics (MHD) model may not capture correctly celestial mechanics.

Using COBRA, our 1MA, 100ns current rise time pulsed-power machine, we can produce plasma with densities on the order of $$10^{20} cm^{-3}$$ and temperatures as high as 100 eV (that is 1 millions degrees kelvin). We also couple our experimental research to numerical code development to highlight which physical models are adequate. We use the PERSEUS code for this research. For instance we discovered recently that the Hall term impact noticeably the plasma dynamics of highly collimated plasma jets. We argued in a recent publication that Hall physics is expressed in astrophysical plasma jets.