Yes. Using the JsonConvert class which contains helper methods for this precise purpose:

// To convert an XML node contained in string xml into a JSON string   
XmlDocument doc = new XmlDocument();
doc.LoadXml(xml);
string jsonText = JsonConvert.SerializeXmlNode(doc);

// To convert JSON text contained in string json into an XML node
XmlDocument doc = JsonConvert.DeserializeXmlNode(json);

Documentation here: Converting between JSON and XML with Json.NET

json:Array='true' isn't going to give you the result you want in this situation. This attribute is intended to signal that you want a particular XML element to be treated as an array when it is converted to JSON in the case that there is only one of them. If there are multiple of a particular XML element, they will automatically be treated as an array. So in your case, the multiple Encounter elements will become an array inside the single Encounters object. It looks like you actually want to flatten this down one level. Json.Net does not have a way to do this using attributes in the XML. So there are three possible approaches I can see to solve this:

1. Manipulate the XML before converting it to JSON
2. Manipulate the JSON after converting it from XML
3. Write a custom XML-to-JSON converter to do what you want.

I think approach 2 is probably the easiest using the LINQ-to-JSON API (JObjects):

string xml =
@"<Container>
  <Encounters>
    <Encounter>
      <a>a1</a>
      <b>b1</b>
    </Encounter>
    <Encounter>
      <a>a2</a>
      <b>b2</b>
    </Encounter>
  </Encounters>
</Container>";

// Convert XML to a JObject
JObject root = JObject.Parse(JsonConvert.SerializeXNode(XElement.Parse(xml)));

// Move the array of Encounter objects up one level
JProperty encounters = ((JObject)root["Container"]).Property("Encounters");
encounters.Value = encounters.Value["Encounter"];

// Output the JSON
string json = root.ToString();
Console.WriteLine(json);

Output:

{
  "Container": {
    "Encounters": [
      {
        "a": "a1",
        "b": "b1"
      },
      {
        "a": "a2",
        "b": "b2"
      }
    ]
  }
}

Fiddle: https://dotnetfiddle.net/kk1Exr

When a property starts with @ you need to alias it.

For Json.net

[JsonProperty("@someVar")]
public int AliasNameGoesHere { get; set; }

For System.Text.Json

[JsonPropertyName("@someVar")]
public int AliasNameGoesHere { get; set; }

Sometimes we just want to make it harder than it is ...

var xml = new XmlDocument();
xml.LoadXml("<person><name>John</name></person>");
Response.ContentType = "application/json";
Response.Write(Newtonsoft.Json.JsonConvert.SerializeObject(xml));

What I did wrong was to serialize the XML into a string and then serialize it again.