how cathodic protection(CP) can change pitting corrosion rate? I think CP can increase pitting grow rate because the pittings create and grow by creation local anodes on the surface and because of heterogeneous surface. is it correct?
The cathodic protection goal is to keep the structure potential below the pitting potential Epitting and about or lower the repassivation potential at which active pits repassivat. In this case the structure will remain passive without nucleation of pits. So you are right when the cathodic protection system was designed and/or operated out of the above scope.
Simply, during cathodic protection we intentionally apply negative potential to make the surface cathodic compare to its original open circuit potential (OCP) in the environment under study. In this case, we preferably enhance the tendency of cathodic (reduction processes) reaction on the surface. The occurrence of localized reactions is limited under these conditions. In other words, the oxidation reactions on the preexisting anodic areas (without CP, at OCP) are forcefully reversed (or the positive current flow towards the surface). In addition, the other cations (e.g. H+ in the form of H3O+ (aqueous/soil, depending on pH) may also reduce on the surface. The hydrogen evolution (due to water reduction as a function of pH) may also induce deleterious effects i.e. hydrogen induced cracking/embrittlement.
For more information, depending on the pH of the environment, during cathodic protection, the stability of oxide film (passive film) is very limited. You always select CP conditions after careful determination of the environmental conditions i.e. electrolyte composition, pH, temperature, OCP and nature of the alloy under study. Mostly for active passive alloys, the Epitting exists above the OCP/Ecorr except under some particular conditions, the Epitting may be less than OCP/Ecorr. For example stainless steel (austenitic) in chloride containing solutions at pH < 3, the Epitt exist below the Ecorr. Even though this alloy shows active passive behavior under these conditions and if by any reason, the pit is formed, it may keep growing even at or below the OCP.
Not to mention that cathodically polarized surfaces are less "attractive" to chloride ions, they are slowly transported to the anode in the electrical field. This can be used for the renovation of buildings (steel in concrete) --> electrochemical chloride extraction.
A short answer to your reasoning "is it correct?" is - unfortunately no. Cathodic Protection, when properly applied, does not increase the corrosion rate in pits. Quite the opposite, it reduces corrosion in pits and general corrosion on bare metal surfaces.
The first question "how cathodic protection(CP) can change pitting corrosion rate?", requires some assumptions about your application area and the initial conditions before answering.
Very generally, in cathodic protection the electrical current is directed towards the metal surface of the working electrode (metal which is to be protected). Or more precisely, positive ions flow towards the WE surface, negative ions and the electrons away from the WE metal surface. Over time, this current flow creates the potential difference between the WE surface and the surrounding electrolyte, in such a way that it suppresses the emission of positive metal ions from the crystal lattice of the WE, that is reduces corrosion of the WE.
The important point is to distinguish between the periods prior to the activation of CP, the period of CP polarisation (transition from unprotected to protected) and the steady state afterwards during which CP is providing constant protection.
Initial conditions for the above periods may include cases with or without pitting (and general) corrosion already occurring prior to the activation of CP.
If your application is in the laboratory studying samples in the corrosion cell these periods are easily observable, and you can verify even visually that the CP as a method is effective in reducing pitting corrosion.
If your application is in the real world protecting infrastructure in seawater, soil or concrete, it is more difficult and more time consuming to confirm the effectiveness of CP observing those three periods.
Also, there are other influencing factors that may hide, or even negate, the corrosion protection provided by CP systems employed. Most prominent is the flow of stray currents (of various origins) in the electrolyte surrounding the metal structure. Flow of uncontrolled both DC and induced AC currents through the structure may overcome the beneficial application of CP and cause pitting on bare metal surfaces at electrical current exit point. These influences are affecting, for instance, coated pipelines in soil near high voltage AC power lines, reinforced concrete in soil close to DC powered rail transport. Also, reinforced concrete in marine environment my suffer pitting around neglected cracks in concrete. All these influences have to be controlled and rectified for the CP to provide effective corrosion protection to the whole metal structure.
I hope this simplified summary of CP will help you in your work with pitting corrosion.
Generally CP reduce the corrosion rate, even in the pitting form. When we talk about CP we may talk about different material in different environment. Just in the some cases that the alkalinity has harmful effect you may expect another result from the CP, such as Al. But as a rule of thumb CP reduce the corrosion, especially for steel in different environment. One good example is Pedeferri's diagram that published in ISO standard and some other reference books. One of them is: