0 3 6 9 12 15 0.00 0.25 0.50 0.75 1.00 1.25  = 0.644 $_{c}$ = 36 0 (Nb) = 1.42 meV NbAu $_{(}$Φ) / $^{ν}$ $_{(}$Φ max ) max 3 = R R + d ). Another class includes the trajectories whose spectra are formed by collisions with the dielectric only, i.e., the trajectories with α > α$_{c}$ . The two groups of tra- jectories produce significantly different spectra of quasi- particles. The distinctions are particularly obvious in the presence of the magnetic field. The trajectories with α ≲ α$_{c}$ form a spectrum of Andreev levels which con- tains an integral of the vector potential field. The spec- trum characterizes the magnetic flux through the area of the triangle between the quasiparticle trajectory and the part of the NS boundary. It also determines the mag- nitude of the screening current produced by ”particles” and ”holes” in the N layer. These states are responsible for the reentrant effect. The trajectories with α > α$_{c}$ do not collide with the NS boundary. The states induced by these trajectories are practically similar to the ”whisper- ing gallery” type of states appearing in the cross section of a solid normal cylinder in a weak magnetic field [13], [14]. The size of the caustic of these trajectories is of the order of the cylinder radius, i.e., they correspond in high magnetic quantum numbers. The spectrum thus formed carries no information about the parameters of the su- perconductor, and it is impossible to meet the resonance condition in this case. These states make a paramagnetic contribution in the thermodynamics of the NS structure but their amplitude is small ( ∼ 1 / ( k$_{F}$ · R ) ). It is there- fore discarded from further consideration. Our interest will be concentrated on the trajectories with | α | ≤ α$_{c}$ . The spectrum of quasiparticles of the NS structure can be obtained easily using the multidimensional quasiclas- sical method generalized for the case of the Andreev scat- tering in the system [15], [16]. After collision with the NS boundary the ”particle” transforms into a ”hole”. The ”hole” travels practically along the path of the ”particle” but in the reverse direction ( Fig.1 ). The spectrum was derived by quantizing the adia- batic invariant 1 2 π ∮ ⃗ P · d⃗ s , where ⃗ P = ⃗ p + e c ⃗ A , ⃗ A = (0 , A$_{y}$ ( x ) , 0), ⃗ P$_{0}$ = ⃗ p$_{0}$ − | e | c ⃗ A for a ”particle” and ⃗ P$_{1}$ = ⃗ p$_{1}$ + | e | c ⃗ A for a ”hole”. Note that each collision with the NS boundary multiplies the wave function amplitude of the quasiparticle by a factor of exp ( − i arccos( E/ Δ)). Let L 0 be the length of the quasiparticle trajectory be- tween the collisions at the boundaries of the N layer. We thus [8], [9] arrive at the expression for the spectrum of the Andreev levels in the NS structure: FIG. 2: The dependence of the density of states of the NS structure on the magnetic flux Φ ( E = E F = 0 ). Normal- ization was performed for the flux Φ max corresponding to the highest value of ν (Φ) ( Φ max ≈ 2 . 175 ). tion from the normal to the boundary ( Fig.1 ). In this case the first class contains the trajectories with α vary- ing within the range − α$_{c}$ ≤ α ≤ α$_{c}$ ( α$_{c}$ is the angle at which the trajectory touches the NS boundary, sin( α$_{c}$ ) E$_{n}$ ( q, α, Φ) = π ℏ v$_{L}$( q ) L 0 [ n + 1 π arccos ( E$_{n}$ ( q, α, Φ) Δ ) − tan ( α ) π Φ ] . (1) Here v$_{L}$( q ) = √ p 2 F − q $^{2}$/m $^{∗}$, L 0 is length of the quasi- particle trajectory, p$_{F}$ is the Fermi momentum, q is the quasiparticle momentum component along the cylinder axis ( | q | ≤ p$_{F}$ ), m ∗ is the effective mass of the quasipar- ticle, and Φ$_{0}$ = hc/ 2 e is the superconducting flux quan- tum. The factor Φ appearing in the last term in Eq. (1)