# How to choose $\beta$ in Gaussian derivative component of DRAG pulse?

From definition of the DRAG pulse it is: $$f(x)=Gaussian+1j*\beta*(-(x-duration/2)/\sigma^2)Gaussian,$$

where $$Gaussian(x, amp, \sigma)=amp*e^{-(1/2)*(x-duration/2)^2/\sigma^2}$$.

If I try it in Python (for $$\beta=$$1e-6):

import numpy as np
import matplotlib.pyplot as plt

t = np.arange(0,8e-6,10e-9)
amp = 1
sigma=1e-6
tc = 8e-6

gaussian = amp*np.exp(-0.5*(t-tc/2)**2/sigma**2)

beta = 1e-6

drag_component = beta*(-(t-tc/2)/sigma**2)*gaussian


I get:

but if I try to set the amplitude of derivative part equaled to the Gaussian ($$\beta$$=1):

the result is strange. How to choose $$\beta$$, what it's meaning and on what it depends?