I will have the white smoke on acceleration processing (whene the motor turn ) and the compressor is not working (no Acceleration speed )
White smoke is most likely to be oil- so you want to check your gaskets and seals. Can you smell burnt oil?
Another possibility is antifreeze or coolant, so if you don't smell oil these are something else to check.
Actually just found an interesting chart which has a list of possible symptoms and causes. If you look at the list and exclude black smoke options, most are engine oil or turbo oil.
Less likely, but is there any chance you have water in your fuel? It would not smell, and would be easy to test by buying from a different gas station. Could also be the answer if you're noticing this more often in cold/humid weather, when water vapor is more likely to condense into fog.
Watch out to not have oil in the coolant or vice-versa. Check the oil level and coolant level and their quality. Usually a head gasket could be a cause of this.
Combining this with "no acceleration speed" this could mean a timing issue too. Maybe the engine timing is not well set and the combustion is not done properly. This means unburned fuel and lots of smoke. I had this once, almost one tooth slipped from the timing belt and had the same problems.