In this sentence, the key phrase is "off the charts", which is an idiom or expression. This expression is supposed to make you think of a "line chart", a measurement of something over time. For example, let us imagine we are measuring the temperature outside every day, and placing each measurement on a line graph (the chart).
My chart is labeled so that the bottom of the chart is "freezing" temperature, or 0 degrees Celsius, known as 32 degrees Fahrenheit in the USA. The top of the chart is the hottest it ever gets around here, labeled 35 degrees Celsius, or 95 degrees Fahrenheit. However, this summer, one day, we measure an amazing 38 degrees Celsius (100 degrees Fahrenheit)! This is hotter than our chart actually allows us to draw, so it is "off the chart"!
In your quotation, Davidson is not measuring temperature, but his happiness. He is happier than the chart expected was possible, so his "brainwaves were off the happiness charts".