My question is, somebody knows if a fermi gas (degenerate electrons) can increase or decrease de total magnetic field due to an influence of an external magnetic field
To know the total magnetic field requires calculating the magnetic susceptibility of the material, in this case that 'material' is a Fermi gas. The magnetic response of a fermi gas (ie: no correlations between electrons) in the presence of a magnetic field is well known. It will consist of two contributions. The first is Pauli paramagnetism. This is the spin response of the electrons. In terms of energy, Pauli paramagnetism is due to the external field producing a finite energy difference between quantized spin up and spin down states of the electrons. The Pauli exclusion principle requires that electrons in the Fermi sea ignore this perturbation. However, near the Fermi surface the electrons spins can polarize in response to this field. In a constant field the Pauli contribution to the magnetic susceptibility is given by:
$$\chi_{P} = \frac{3n\mu_{0}\mu_{B}^{2}}{2E_{F}}$$
The second contribution is Landau diamagnetism. This is the orbital response of the electrons. The simplest picture is that the magnetic field drives the electrons into orbits around the field direction. This is very much akin to the production of a current in a wire loop upon application of a magnetic field, and just like in the wire loop, the induced orbits will try and cancel the field. This is why the orbital contribution is a diamagnetic response. In terms of energy, the B=0 electron states produce a spherical volume that is discreetized into ##k_{x}##, ##k_{y}##, and ##k_{z}## boxes (ie: just our good old fashioned free electron gas model). When a field is applied, say along the z direction, the ##k_{x}## and ##k_{y}## momenta condense into degenerate nested cylinders oriented along the z-direction, so called Landau levels. The production of these levels changes the total energy of the system. Namely, the ##k_{x}## and ##k_{y}## values near the Fermi surface must adjust their energy to the nearest Landau level upon application of a magnetic field. The Landau contribution to the magnetic susceptibility in a constant field can be derived by working through the energetics of this picture and is given by:
$$\chi_{L} = -\frac{1}{3}\chi_{P}$$
Again, the results are for a free electron gas, if correlations between electrons must be taken into account than this will change things, enough so that I don't think a PhysicsForums post will give much traction, it will take a lot of reading and tailored application with your specific problem in mind; you will need band structure and so, at the very least I expect, you will also need DFT. I will state the simplest modification though. Correlations will renormalize the electrons effective mass ##m^{*}## and the net result is that the Landau susceptibility will now scale as
$$\chi_{L} = -\frac{1}{3}\left(\frac{m_{e}}{m^{*}}\right)^{2}\chi_{P}$$
Thus, if the effective mass is small enough, then it can cause the diamagnetic contribution to be larger than the paramagnetic and your total field will reduce.
Also the magnetic field is not constant at all, because is generated via plasma convection and it hve many turbulence and other phenomena
This is going to make your life much harder, because they do have an effect. Note that I was very careful to state that the above results were for a constant magnetic field. In the presence of a wavevector-dependent ##\mathbf q## and frequency-dependent ##\omega## magnetic field then the magnetic susceptibility becomes a tensor of the form:
$$ \mathbf\chi\left(\mathbf q, \mathbf k; \Omega, \omega\right)$$
where ##\mathbf k## and ##\Omega## are the Fourier domain of the spatial and temporal change of the electron magnetization in response to the applied field. Things can become a bit tough. How far down the rabbit hole you have to go is dependent on the problem at hand. Good luck.
