By introducing a parameter defined as an azimuthal mode number

the classical Creedon theory is generalized to two-dimensional situations

to describe the nonaxisymmetrical magnetic insulation caused by azimuthally asymmetrical distributions of feed currents within cavity in induction voltage adders（IVA）. A two-dimension Creedon model is developed

and the relationship of electrical parameters of the magnetic insulation（i.e.

electric filed

magnetic flux density

electron density

and electron sheath edge） depending on the relativistic factor

γ（r

θ）

is derived. Given some boundary conditions

e.g.

the azimuthal distributions of magnetic flux density on the cathode

the physical model is numerically solved

and the two-dimensional distribution of characteristics of the nonaxisymmetrical magnetic insulation of IVA is acquired. It is found that

as the magnetic flux density on the cathode satisfies the cosine distribution

the azimuthal distributions of electron sheath edges approximate the Gauss function. At the azimuthal positions close to injection points

the thickness of the electron sheath is much thinner due to the stronger magnetic flux density

whereas the electron density is lower. The azimuthal uniformity of the magnetic flux density on the anode is much better than that of cathode

and the phase between them is about 180°

which are in agreement with the experiments on the RITS-3 facility. In addition

the physical model and numerical solutions presented in this paper are capable of describing the nonaxisymmetrical magnetic insulation caused by the off-center of inner electrodes in the long magnetically insulated transmission lines（MITL）.