Neutron flux for uniform cylinder¶

Neutron flux for the uniform cylindrical reactor of radius \(r_0\) and height \(h_0\) depends on the radial distance \(r\) and axial coordinate \(z\). A cylindrical coordinate system is assumed, such that the cylinder’s axis of rotation is the \(z\)-axis.

Links:

NuclearPower, see end of page.

dimension_factor¶: Dimension factor that appears as a coefficient in the solution to the differential equation. See neutron_flux.

Symbol:: Phi_0
Latex:: \(\Phi_{0}\)
Dimension:: 1/(area*time)

radial_distance¶: distance_to_axis within the cylindrical coordinate system of the cylinder.

Symbol:: r
Latex:: \(r\)
Dimension:: length

axial_coordinate¶: height within the cylindrical coordinate system of the cylinder.

Symbol:: h
Latex:: \(h\)
Dimension:: length

radius¶: radius of the cylinder.

Symbol:: r_0
Latex:: \(r_{0}\)
Dimension:: length

height¶: height of the cylinder.

Symbol:: h_0
Latex:: \(h_{0}\)
Dimension:: length

neutron_flux¶: neutron_flux at a point with coordinates radial_distance and axial_coordinate.

Symbol:: Phi
Latex:: \(\Phi\)
Dimension:: 1/(area*time)

law¶

Phi = Phi_0 * besselj(0, 2.405 / r_0 * r) * cos(pi / h_0 * h)

Latex:: \[\Phi = \Phi_{0} J_{0}\left(\frac{2.405}{r_{0}} r\right) \cos{\left(\frac{\pi}{h_{0}} h \right)}\]