How to start and stop a process in a Jest automated test?

I am trying to write a jest automated test that starts my node server, attempts to connect to it, and then stops the node server.

import fetch from 'node-fetch';

jest.setTimeout(100000);

test('starting the root-config opens a webserver on port 9000', async () => {
  // given we have started the root-config project
  var serverProcess = require('child_process').spawn('npm run start')

  // when we request http://localhost:9000/
  var response;
  var done = false;
  while(!done) {
    try {
      response = await fetch("http://localhost:9000");
      done = true;
    } catch(e) {
    }
  }

  // terminate the server process when we're done getting a response
  serverProcess.kill('SIGKILL');

  // then we will get a 200 response
  expect(response.status).toBe(200);
});

This will reliably start the server, but it rarely manages to stop the server and Jest refuses to terminate.