Electric/Energy Particle System

Is it possible to get this effect in unity? How can I do it? I assume it is a particle system and line renderer

https://www.youtube.com/watch?v=rR6aztrOe2s

Here is what I have so far. I have a start position and an end position. What Can I do to make random points between point A and point B? I am not sure what I should put in my Vector3() so the points are random, but not too far from the line...

 using UnityEngine;
 using System.Collections;

 [RequireComponent(typeof(LineRenderer))]

 public class Electricity : MonoBehaviour {

     public int minPoints = 2;
     public int maxPoints = 10;
     public Transform startPosition;
     public Transform endPosition;

     protected LineRenderer lr;
     protected int points;

     // Use this for initialization
     void Start () {
         lr = GetComponent<LineRenderer>() as LineRenderer;
     }
     
     // Update is called once per frame
     void Update () {
         int i = 0;
         points = Random.Range(minPoints, maxPoints);
         lr.SetVertexCount(points);
         while (i < points) {
             Vector3 pos = new Vector3();
             lr.SetPosition(i, pos);
             i++;
         }
     }
 }