PTC: Full and Drift Particle Orbit Tracing Code for α Particles in Tokamak Plasmas

Fusion born α particle confinement is one of the most important issues in burning plasmas,such as ITER and CFETR.However,it is extremely complex due to the nonequilibrium characteristics,and multiple temporal and spatial scales coupling with background plasma.A numerical code using particle orbit tracing method(PTC)has been developed to study energetic particle confinement in tokamak plasmas.Both full orbit and drift orbit solvers are implemented to analyze the Larmor radius effects on α particle confinement.The elastic collisions between alpha particles and thermal plasma are calculated by a Monte Carlo method.A triangle mesh in poloidal section is generated for electromagnetic fields expression.Benchmark between PTC and ORBIT has been accomplished for verification.For CFETR burning plasmas,PTC code is used for α particle source and slowing down process calculation in 2D equilibrium.In future work,3D field like toroidal field ripples,Alfven and magnetohydrodynamics instabilities perturbation inducing α particle transport will be analyzed.

Linear recurring sequences and subfield subcodes of cyclic codes

Linear recurring sequences over finite fields play an important role in coding theory and cryptography. It is known that subfield subcodes of linear codes yield some good codes. In this paper, we study linear recurring sequences and subfield subcodes. Let Mqm(f(x)) denote the set of all linear recurring sequences over Fqm with characteristic polynomial f(x) over Fqm . Denote the restriction of Mqm(f(x)) to sequences over Fq and the set after applying trace function to each sequence in Mqm(f(x)) by Mqm(f(x)) | Fq and Tr( Mqm(f(x))), respectively. It is shown that these two sets are both complete sets of linear recurring sequences over Fq with some characteristic polynomials over Fq. In this paper, we firstly determine the characteristic polynomials for these two sets. Then, using these results, we determine the generator polynomials of subfield subcodes and trace codes of cyclic codes over Fqm .

On Reed-Solomon Codes

The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory.The main problem is to compute the error distance of a received word.Using the Weil bound for character sum estimate,Li and Wan showed that the error distance can be determined when the degree of the received word as a polynomial is small.In the first part,the result of Li and Wan is improved.On the other hand,one of the important parameters of an error-correcting code is the dimension.In most cases,one can only get bounds for the dimension.In the second part,a formula for the dimension of the generalized trace Reed-Solomon codes in some cases is obtained.