Once the plasma is in the tokamak reactor how long does it take until fusion starts to begin? I found that it must reach 150000000 degrees so, how long does it take for the plasma to reach this temperature? Is there a graph of time against temperature for the inside of a tokamak and which reactor reaches this fastest?
As others have mentioned, the speed is not really a key issue when we operate tokamak reactors. Plasma parameters respond in a fast timescale to inputs of external heating sources and stability control schemes.
A plateau of high temperature is reached as soon as the plasma current, radio frequency power and neutral beam injection power all reach their respective plateaus, provided control mechanisms (e.g. resonant magnetic perturbations) have also been applied. In most research reactors today, such plateaus are typically reached within just a couple of seconds.
As an example you can see this picture from last year's record temperature-duration experiment of the EAST tokamak in China, in which an electron temperature of 50 million degrees K (three times that of the core of the sun) was maintained for around 100 seconds. There you may observe how fast the temperature plateau was reached.