 	        //transform compute n and logn
         for(unsigned i=0; i<2; i++)
         {
-            dg::blas1::transform( y[i], npe[i], dg::EXP<value_type>()); // 1+ \tilde{N}
-            dg::blas1::pointwiseDot(npe[i],profne,npe[i]); //N
+            dg::blas1::transform( y[i], npe[i], dg::EXP<value_type>()); // = exp(bar delta N) = 1+tilde N
+            dg::blas1::pointwiseDot(npe[i],profne,npe[i]);              // = N
             dg::blas1::transform( npe[i], logn[i], dg::LN<value_type>());
         }  
         

        if (p.hwmode==1) {
            polavg(logn[0],lambda);       //<ln(ne)> 
            polavg(phi[0],phiavg);        //<phi>
            dg::blas1::axpby(1.,phi[0],-1.,phiavg,phidelta); // delta(phi) = phi - <phi>
	    
/*	    dg::blas1::pointwiseDivide(nedelta,neavg,lambda); // delta(phi) = phi - <phi>
	    polavg(lambda,omega);       //<ln(ne)> 
	    dg::blas1::axpby(1.,lambda,-1.,omega,nedelta); // delta(ln(ne)) = ln(ne)- <ln(ne)>   */      
	    
            dg::blas1::axpby(1.,logn[0],-1.,lambda,lognedelta); // delta(ln(ne)) = ln(ne)- <ln(ne)>         
            dg::blas1::axpby(1.,phidelta,p.tau[0],lognedelta,omega); //omega = phi - lnNe

            //---------- perp dissipation 
            dg::blas2::gemv( lapperp, y[i], lambda);
            dg::blas2::gemv( lapperp, lambda, omega);//nabla_RZ^4 N_e
            dg::blas1::pointwiseDot( npe[i], omega, omega);//nabla_RZ^4 N_e
            Dperp[i] = -z[i]* p.nu_perp*dg::blas2::dot(chi, w2d, omega);  //  tau_z(1+lnN)+phi) nabla_RZ^4 \tilde N
        }                
        //compute the radial electron density  transport
